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

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Re: In the figure above, is the area of triangular region ADE equal to the [#permalink]
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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]
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]
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]
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Solution

Steps 1 & 2: Understand Question and Draw Inferences
We are given a quadrilateral ABCD that includes
• 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 × 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]
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

Attachment:
2019-04-26_1818.png

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]
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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

Attachment:
2019-04-26_1818.png

Solution: Combo Problem in Disguise

A) Sufficient
B) Sufficient

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Re: In the figure above, is the area of triangular region ADE equal to the [#permalink]
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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]
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]
Top Contributor
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

Attachment:
2019-04-26_1818.png

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

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

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

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

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

The answer is $$D$$
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In the figure above, is the area of triangular region ADE equal to the [#permalink]
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

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]
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

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?