A quadrilateral has a perimeter of 16. Which of the following alone

Question

A quadrilateral has a perimeter of 16. Which of the following alone would provide sufficient information to determine the area of the quadrilateral.

A)The quadrilateral contains equal sides.

B)The quadrilateral is formed by combining two isosceles right triangles.

C) Two pairs of congruent angles are in a 2:1 ratio.

D) The width is 4o% of the length and all angles are of equal measure.

E) If the perimeter was decreased by 50%, the area would decrease by 25%.

adityapareshshah · Answer

The answer has to be D.

The quadrilateral described in option D is a rectangle.
Reasons:-
1. All angles are equal.(Given) Hence each side is of 90 degree. So it has to be a square or a rectangle.
2. The width is 4o% of the length----> Implies it is not a square.---------------------------------------------------Equation (1)

We know the perimeter.

2(l +b)= 16.
l + b= 8.
Using equation 1, l and b can be calculated and the area will be = l * b.

matthewsmith_89 · Answer

I think the answer is D
D is saying that the quadrilateral is a rectangle

stonecold · Answer

Hi  chetan2u 
Can you please provide a solution to this one.
I get why D is the answer.
But can't B and C be the answer choice.

Thanks 
Stone Cold

mogarza08 · Answer

While I agree that D is accurate and leaves us with a rectangle, I initially picked B thinking that this would be a square (combining 2 45 45 90 triangles forming a square). So, I would also like to know why B is wrong if someone can explain.

Thanks!

Thanks!

EgmatQuantExpert · Answer

For Option B, the two diagrams are given below. According to me, since we can get two different type of quadrilateral, we cannot answer what would be the area with surety. https://e-gmat.com/blogs/wp-content/uploads/2017/04/GC2-e1493578009638.jpg Thanks, Saquib Quant Expert e-GMAT Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

https://e-gmat.com/blogs/wp-content/uploads/2016/12/NP-Free-Trial-e1481107541356.png

EgmatQuantExpert · Answer

Even in the case of Option C, we can get two different types of quadrilateral and hence the area would differ and with the limited information given, I don't think we can even find the area, with just the angles and sum of lengths.

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

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https://e-gmat.com/blogs/wp-content/uploads/2016/12/NP-Free-Trial-e1481107541356.png

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A quadrilateral has a perimeter of 16. Which of the following alone

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A quadrilateral has a perimeter of 16. Which of the following alone

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