Vincen wrote: ↑Fri Aug 06, 2021 7:34 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
Cheers,
Brent
