12 Days of Christmas GMAT Competition - Day 10: Is the perimeter of a

Is the perimeter of a rectangle more than 60 cm ?

(1) The area of the rectangle is 226 cm^2.
(2) The length of a diagonal of the rectangle is 30 cm.

L + W > 30 Y/N?


1) Area = 226 = LxW

We have (L+W)^2 >= 4LW = 4x226 > 4x225 = (2x15)^2 --> L + W > 30 --> Yes --> Sufficient
Notice that: (L+W)^2 >= 4LW or (L-W)^2 >= 0 is always true


2) Diagonal = 30

Let's consider half of that rectangle, we will have L + W > Diagonal = 30 (according to side inequalities in a certain triangle)
--> Yes --> Sufficient

Correct answer: D

statement 1:

Area is 226 cm^2

assume Square, l=b
then l^2 = 226
l=15.xx (approx)

so perimeter 4l is more than 60. For rectangle then l is greater than breadth. so obviously perimeter is greater than 60

Hence Statement 1 is sufficient

Statement 2:

hypotenuse is 30. That means sum of two sides should be greater than 30. Hence perimeter will be greater than 60.

So Statement 2 is also sufficient.


Hence option D

Is the perimeter of a rectangle more than 60 cm ?

(1) The area of the rectangle is 226 cm^2.

Concept: For a given area of quadrilateral, a square would have the smallest perimeter.
So, let us assume that the rectangle is actually a square.
If area (of square) = 226, side = 15.033 (approx)
So the perimeter would be slightly greater than 60 cm.
If a square has a greater perimeter than 60, a rectangle would definitely have a perimeter > 60
Sufficient.


(2) The length of a diagonal of the rectangle is 30 cm.

If length = l and Breadth = b
\(l^2 + b^2\) = 900
Suppose: b= 20, then l= 22.36. (perimeter 84.72 > 60)
Suppose: b= 10, then l= 28.28. (perimeter 76.56 > 60)
Suppose: b= 1, then l= 29.98. (perimeter 61.96 > 60)
Now Suppose b = 0.0001, then l = 29.9999983333 (perimeter 60.000196 > 60)
As one of the sides gets smaller and smaller, the perimeter gets closer to 60.
HOWEVER, the perimeter will ALWAYS be > 60,
This is also sufficient

Both statements individually sufficient.
Answer D

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.