ardz24 wrote:What is the perimeter of a rectangle if the ratio of its width to its length is 3 to 4?

(1) The width of the rectangle is 6.
(2) The area of the rectangle is 48.

Target question: What is the perimeter of the rectangle?

Given: Ratio of its width to its length is 3 to 4?
Let W = width of the rectangle
Let L = length of the rectangle
We can write: W/L = 3/4

Statement 1: The width of the rectangle is 6
If the width = 6, we can write: 6/L = 3/4
At this point, we COULD solve this equation for L (the length), but we won't because that would be a waste of time.
We need only recognize that we COULD determine the length, at which point we'd have both dimensions, in which case we COULD determine the perimeter.
Since we COULD answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The area of the rectangle is 48
In other words, LW = 48
Divide both sides by W to get: L = 48/W

It is also GIVEN that W/L = 3/4
We can take this equation and cross multiply to get: 4W = 3L
Now replace the L above with 48/W to get: 4W = 3(48/W)
Simplify: 4W = 144/W
Multiply both sides by W to get: 4W² = 144
Divide both sides by 4 to get: W² = 36
So, EITHER W = 6 OR W = -6
Since W must be POSITIVE, we can be certain that W = 6
If W = 6, then it must be the case that L = 8 (since the ratio of width to length is 3 to 4)
This means the perimeter = 6 + 6 + 8 + 8 = 28
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent