Perimeter of rectangle

mals24 wrote:Does rectangle A have a greater perimeter than rectangle B?

1. The length of a side of rectangle A is twice the length of a side of rectangle B.

2. The area of rectangle A is twice the area of rectangle B.

OA after a few discussions.

As always, let's start by jotting down the relevant formulas on our scratch paper:

Area = l * w
perimiter = 2l + 2w

(1) we know that 1 of the sides of A is twice one of the sides of B.

However, we know nothing about the other sides, so (1) is insufficient.

(2) Knowing the relationships between the areas does NOT help us determine which has a bigger perimiter.

For example, A could be a 6*5 rectangle and B could be a 3*5 rectangle, in which case A would have a bigger perimiter.

On the other hand, A could be a 6*5 rectangle and B could be a (.01)*(1500) rectangle, in which case B would have a bigger perimiter.

Therefore, (2) is also insufficient.

For combining, let's define some variables to make the discussion simpler:

Let p and q be the sides of Rectangle A and let x and y be the sides of Rectangle B.

From (2), we know that pq = 2(xy).
From (1), we know that one of p or q is 2 times one of x or y. We really don't care which is which, so let's say that p = 2x.

Subbing into (2), we now get:

2xq = 2xy
q = y

So, we know that one side of Rectangle A is bigger than a side of Rectangle B and the other two sides of the rectangles are equal. Therefore, Rectangle A must have a greater perimiter than Rectangle B. Together, we get a definite "yes" answer: choose (C).

Nice question, let me try:

A has two sides a & b
B has two sides k & l

Question is : Is a+ b > k + l

Statement 1) a=2k

2k + b > k + l

k > l - b ; since we don't know anything about l and b - INSUF

Statement 2 ) ab = 2kl

ab = 2kl can be - lets say - 64

a = 16 , b = 4
k = 32 , l = 1

a+b < k + l

OR

a = 32 , b = 2
k = 16 , l = 1

a+b > k + l

Insuf

Statement 1 & 2

ab = 2kl and a=2k

2k x b = 2k x l

b=l

since b=l and a=2k

Rectangle A have a greater perimeter than rectangle B.

Hence, C

Hey Stuart thanks for reply.

But I'm still confused with statement 1.

It says the length of A is greater than the length of B.
So won't the perimeter of A be bigger than that of B.

I used to think the length of the a rectangle is the longest side of a rectangle.

So thats the logic I used. Since the length of a rectangle is the longest side, the widths of both the rectangles will be less than the length of rectangle A and hence A's perimeter is greater than that of B.

For instance if Length of rect A = 36
Length of rect B = 12
So no matter what the width of A & B the perimeter of A will be greater. Using this logic I picked option A.

mals24 wrote:Hey Stuart thanks for reply.

But I'm still confused with statement 1.

It says the length of A is greater than the length of B.
So won't the perimeter of A be bigger than that of B.

I used to think the length of the a rectangle is the longest side of a rectangle.

So thats the logic I used. Since the length of a rectangle is the longest side, the widths of both the rectangles will be less than the length of rectangle A and hence A's perimeter is greater than that of B.

For instance if Length of rect A = 36
Length of rect B = 12
So no matter what the width of A & B the perimeter of A will be greater. Using this logic I picked option A.

The statement says that the length of a side of Rectangle A is twice the length of a side of Rectangle B. Based on this information, it's possible that it's referring to the long side of A and the short side of B.

If the statement had referred to the length of the rectangles, your characterization would be more accurate.

OMG i missed this point completely

Thanks a ton Stuart for pointing it out.

Btw for those who still din't figure out OA is C.