Is the perimeter of square \(S\) greater than the perimeter of equilateral triangle \(T?\)

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Is the perimeter of square \(S\) greater than the perimeter of equilateral triangle \(T?\)

(1) The ratio of the length of a side of \(S\) to the length of a side of \(T\) is \(4:5.\)
(2) The sum of the lengths of a side of \(S\) and a side of \(T\) is \(18.\)

Answer: A

Source: Official Guide

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Vincen wrote:
Wed Nov 18, 2020 11:30 am
Is the perimeter of square \(S\) greater than the perimeter of equilateral triangle \(T?\)

(1) The ratio of the length of a side of \(S\) to the length of a side of \(T\) is \(4:5.\)
(2) The sum of the lengths of a side of \(S\) and a side of \(T\) is \(18.\)

Answer: A

Source: Official Guide
Target question: Is the perimeter of square S greater than the perimeter of equilateral triangle T?

Statement 1: The ratio of the length of a side of S to the length of a side of T is 4:5.
Let x = the length of EACH side of the square
Let y = the length of EACH side of the equilateral triangle

So, we can write: x/y = 4/5
Cross multiply to get: 5x = 4y
Divide both sides by 5 to get x =4y/5
We can also write: x = 0.8y

The perimeter of the equilateral triangle = y + y + y = 3y
The perimeter of the square = x + x + x + x = 4x

Since we now know x = 0.8y, we can replace x with 0.8y to get:
The perimeter of the square = 0.8y + 0.8y + 0.8y + 0.8y = 3.2y

Since the perimeter of the equilateral triangle = 3y, and the perimeter of the square = 3.2y, the answer to the target question is YES, the perimeter of square S is greater than the perimeter of equilateral triangle T
Statement 1 is SUFFICIENT

Statement 2: The sum of the lengths of a side of S and a side of T is 18.
There are several scenarios that satisfy statement 2. Here are two:
Case a: Each side of the square has length 17, and each side of the equilateral triangle has length 1. So the perimeter of the square = 17 + 17 + 17 + 17 = 68, and the perimeter of the triangle = 1 + 1 + 1 = 3. In this case, the answer to the target question is YES, the perimeter of square S is greater than the perimeter of equilateral triangle T
Case b: Each side of the square has length 1, and each side of the equilateral triangle has length 18. So the perimeter of the square = 1 + 1 + 1 + 1 = 4, and the perimeter of the triangle = 17 + 17 + 17 = 51. In this case, the answer to the target question is NOT, the perimeter of square S is not greater than the perimeter of equilateral triangle T
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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