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In the figure above, is the area of triangular region ADE equal to the

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Bunuel
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In the figure above, is the area of triangular region ADE equal to the [#permalink] In the figure above, is the area of triangular region ADE equal to the   26 Apr 2019, 07:19
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In the figure above, is the area of triangular region ADE equal to the area of rectangular region ABCD ?

(1) x = 10 and y = 5.
(2) x = 2y


DS17502.01
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DavidTutorexamPAL
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Re: In the figure above, is the area of triangular region ADE equal to the [#permalink] In the figure above, is the area of triangular region ADE equal to the   19 May 2019, 04:53
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Hey nishankjain09,

The answer is almost what pandajee wrote above, with the correction that ABCD might not be a square.
In particular,
Area of ABCD = AD * y
Area of ADE = AD * x / 2.

So to know if the areas are equal, we need to know the ratio between x and y: if x = 2y they are equal and the answer is YES, otherwise the answer is NO.
(1) and (2) both provide this information so are sufficient.

The original explanation was a bit more general -- the area of a rectangle is the product of its adjacent sides and that of the right triangle the product of its legs divided by 2. Since we want to compare the areas, we should start by comparing those sides that we know. As we can compare one of the sides (AD) all we need is information which lets us compare the others (x vs. y)
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Re: In the figure above, is the area of triangular region ADE equal to the [#permalink] In the figure above, is the area of triangular region ADE equal to the   26 Apr 2019, 07:23
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Answer id d as both statements ar3 sufficient independently to reach to a conclusion

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Re: In the figure above, is the area of triangular region ADE equal to the [#permalink] In the figure above, is the area of triangular region ADE equal to the   27 Apr 2019, 04:56
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The Logical approach to comparison is to start with the measurements the shapes share.
Since AD is both the right triangle's leg and the rectangle's side, what we'll be looking for is information on the ratio between the other leg and the other side. Since both statements provide is such information, they are each sufficient on their own.

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Re: In the figure above, is the area of triangular region ADE equal to the [#permalink] In the figure above, is the area of triangular region ADE equal to the   18 May 2019, 22:16
DavidTutorexamPAL
The Logical approach to comparison is to start with the measurements the shapes share.
Since AD is both the right triangle's leg and the rectangle's side, what we'll be looking for is information on the ratio between the other leg and the other side. Since both statements provide is such information, they are each sufficient on their own.

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Can you please explain the answer to the above question in detail?
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Re: In the figure above, is the area of triangular region ADE equal to the [#permalink] In the figure above, is the area of triangular region ADE equal to the   19 May 2019, 00:08
nishankjain09
DavidTutorexamPAL
The Logical approach to comparison is to start with the measurements the shapes share.
Since AD is both the right triangle's leg and the rectangle's side, what we'll be looking for is information on the ratio between the other leg and the other side. Since both statements provide is such information, they are each sufficient on their own.

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Can you please explain the answer to the above question in detail?

The main idea is to recognize that the rectangle ABCD is a square. So, we get the value for side AD=y
Area of traingle = 1/2 * x * y
Area of square = y * y

1 & 2 both are sufficient independently as we can compare areas of Triangle and Square with the given information.
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Re: In the figure above, is the area of triangular region ADE equal to the [#permalink] In the figure above, is the area of triangular region ADE equal to the   23 May 2019, 07:02
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Solution


Steps 1 & 2: Understand Question and Draw Inferences
We are given a quadrilateral ABCD that includes
    • ∆ADE and Rectangle ABCD
    • Length of DE = x and DC = y

We need to determine:
    • Whether the area of ∆ADE = area of rectangle ABCD or not.
      Or, 1/2 × AD × DE = AB × BC
      Or, 1/2 × AD × DE = CD × AD (Since ABCD is a rectangle, AB = CD = y and AD = BC)
      Or, 1/2 × AD × x = y × AD
      Or, 1/2 × x = y (Since AD is side length, it cannot be negative. Hence, we can divide both the sides of the inequality by AD)
      Or, x = 2y

    • Therefore, if x = 2y then the answer is Yes, else the answer is No.

With this understanding let us analyse the statements.

Step 3: Analyse Statement 1
“x = 10 and y = 5”
    • 10 = 2 * 5

Since x = 2y, the answer to the question is Yes.
Thus, statement 1 is sufficient to answer the question.

Step 4: Analyse Statement 2
“x = 2y”
Since x = 2y, the answer to the question is Yes.
Thus, statement 2 is sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)
Since we could determine the answer from either of the statements individually, this step is not required.

Hence, the correct answer is option D.

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Re: In the figure above, is the area of triangular region ADE equal to the [#permalink] In the figure above, is the area of triangular region ADE equal to the   23 May 2019, 18:46
Bunuel

In the figure above, is the area of triangular region ADE equal to the area of rectangular region ABCD ?

(1) x = 10 and y = 5.
(2) x = 2y


DS17502.01
Quantitative Review 2020 NEW QUESTION


Show Spoiler
Attachment:
2019-04-26_1818.png

let AD=b

Triangle area= (1/2)*x*b
Rectangular area= y*b

(1) Put values to get both area 5b

(2) Put values to get both area yb.

Both statements independently sufficient, D.
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Re: In the figure above, is the area of triangular region ADE equal to the [#permalink] In the figure above, is the area of triangular region ADE equal to the   24 May 2019, 04:47
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Bunuel

In the figure above, is the area of triangular region ADE equal to the area of rectangular region ABCD ?

(1) x = 10 and y = 5.
(2) x = 2y


DS17502.01
Quantitative Review 2020 NEW QUESTION


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Attachment:
2019-04-26_1818.png

Solution: Combo Problem in Disguise



Wanted: x/2 * AD = AD*y => x = 2y?

A) Sufficient
B) Sufficient

ANSWER: D
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Re: In the figure above, is the area of triangular region ADE equal to the [#permalink] In the figure above, is the area of triangular region ADE equal to the   10 Jun 2020, 15:11
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I don't get it, it says that it's a rectangle, it might be AD>DC.
It doesn't mention anywhere that it is a square.

If it is a rectangle IMO it's E.
Otherwise it's D.
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Re: In the figure above, is the area of triangular region ADE equal to the [#permalink] In the figure above, is the area of triangular region ADE equal to the   07 Nov 2020, 08:19
warrax
I don't get it, it says that it's a rectangle, it might be AD>DC.
It doesn't mention anywhere that it is a square.

If it is a rectangle IMO it's E.
Otherwise it's D.

That's what this question is testing. The figure on the right IS a rectangle, not a square.

If you use the statements and plug in the values given you'll find that the area of triangular region ADE is equal to the are of rectangular region ABCD.

AD and BC could be 5 or 100,000. The area of ADE and ABCD will be equal.
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Re: In the figure above, is the area of triangular region ADE equal to the [#permalink] In the figure above, is the area of triangular region ADE equal to the   16 Dec 2020, 10:25
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Bunuel

In the figure above, is the area of triangular region ADE equal to the area of rectangular region ABCD ?

(1) x = 10 and y = 5.
(2) x = 2y


DS17502.01
Quantitative Review 2020 NEW QUESTION


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Attachment:
2019-04-26_1818.png

Question Asked whether \(\frac{1}{2}x*AD=AD*y\)

(1) Area of the triangle\(=\frac{1}{2}x*AD=\frac{1}{2}10*AD=5AD\)

The area of the rectangle =AD*y=AD*5=5AD

So, \(\frac{1}{2}x*AD=AD*y=5AD\) Sufficient.

(2) Area of the triangle \(=\frac{1}{2}x*AD=\frac{1}{2}2y*AD=yAD\)

The area of the rectangle =AD*y=ADy=yAD

\(\frac{1}{2}x*AD=AD*y\)\(=yAD\) Sufficient.

The answer is \(D\)
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In the figure above, is the area of triangular region ADE equal to the [#permalink] In the figure above, is the area of triangular region ADE equal to the   18 Dec 2022, 14:22
Bunuel

In the figure above, is the area of triangular region ADE equal to the area of rectangular region ABCD ?

(1) x = 10 and y = 5.
(2) x = 2y


DS17502.01
Quantitative Review 2020 NEW QUESTION


Show Spoiler
Attachment:
2019-04-26_1818.png

Bunuel
How would you solve this one? I did the following:

Statement 1:
0.5*b*h=area of triangle --> 0.5*10*h=5h
h*y=area of rectangle --> 5*h=5h
suff.

Statement 2:
Area of triangle: 0.5*x*h=0.5*2y*h=y*h
Area of rectangle: y*h
suff.
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Re: In the figure above, is the area of triangular region ADE equal to the [#permalink] In the figure above, is the area of triangular region ADE equal to the   19 Dec 2022, 04:16
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woohoo921
Bunuel

In the figure above, is the area of triangular region ADE equal to the area of rectangular region ABCD ?

(1) x = 10 and y = 5.
(2) x = 2y


DS17502.01
Quantitative Review 2020 NEW QUESTION


Show Spoiler
Attachment:
2019-04-26_1818.png

Bunuel
How would you solve this one? I did the following:

Statement 1:
0.5*b*h=area of triangle --> 0.5*10*h=5h
h*y=area of rectangle --> 5*h=5h
suff.

Statement 2:
Area of triangle: 0.5*x*h=0.5*2y*h=y*h
Area of rectangle: y*h
suff.

Is the area of triangular region ADE equal to the area of rectangular region ABCD?

    Is 1/2*AD*x = AD*y ?
    Is 1/2*x = y ?
    Is x = 2y ?

So, this is the question! Each statement give an YES answer to this question, so D it is.
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Re: In the figure above, is the area of triangular region ADE equal to the [#permalink]
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