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

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)

Answer id d as both statements ar3 sufficient independently to reach to a conclusion

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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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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.

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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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.

Solution: Combo Problem in Disguise

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

A) Sufficient
B) Sufficient

ANSWER: D

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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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 \(D\)

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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