sandy wrote:
Attachment:
Capture.JPG
In the right triangle above, what is the length of AC?
(A) 9
(B) 10
(C) 12
(D) 13
(E) 15
Since we have a
right triangle, we can apply the
Pythagorean TheoremWhen we do so we get: (x - 1)² + (x + 2)² = (x + 5)²
Expand each square to get: (x² - 2x + 1) + (x² + 4x + 4) = x² + 10x + 25
Simplify left side to get: 2x² + 2x + 5 = x² + 10x + 25
Subtract x² from both sides to get: x² + 2x + 5 = 10x + 25
Subtract 10x from both sides to get: x² - 8x + 5 = 25
Subtract 25 from both sides to get: x² - 8x - 20 = 0
Factor: (x - 10)(x + 2) = 0
So, EITHER x = 10 OR x = -2
We can rule out the solution x = -2, since that would make some of the lengths NEGATIVE
So, it MUST be the case that x =
10AC has length x + 2
So, AC =
10 + 2 = 12
Answer: C
Cheers,
Brent