AbeNeedsAnswers wrote:If x and y are the lengths of the legs of a right triangle, what is the value of xy ?
(1) The hypotenuse of the triangle is 10√2.
(2) The area of the triangular region is 50.
B
Source: Official Guide
Given: x and y are the lengths of the legs of a right triangle
We have something like this:
Target question: What is the value of xy?
Statement 1: The hypotenuse of the triangle is [m]10[square_root]2[/square_root][/m].
There are infinitely-many different right triangles that meet this condition. Here are two:
Case a: x = 10 and y = 10
CHECK: If h = the hypotenuse, then we get 10² + 10² = h²
Solve: 200 = h²
So, h = √200 = 10√2
In this case, the answer to the target question is
xy = (10)(10) = 100
Case b: x = √50 and y = √150
CHECK: If h = the hypotenuse, then we get (√50)² + (√150)² = h²
Solve: 200 = h²
So, h = √200 = 10√2
In this case, the answer to the target question is
xy = (√50)(√150) = √7500 = 50√3
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The area of the triangular region is 50
Area of triangle = (base)(height)/2
So, we can write: (x)(y)/2 = 50
Multiply both sides by 2 to get: xy = 100
So, the answer to the target question is
xy = 100
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
