shasadou wrote:
The sides of a right triangle are consecutive even integers, and the length of the longest side is p. Which of the following equations could be used to find p?
A. (p–4)^2=p^2–(p−2)^2
B. (p–2)^2=(p–4)–p^2
C. p^2+4^2+2^2=6^2
D. (p–2)^2=p^2–(p−1)^2
E. (p+2)^2+(p+4)^2=p^2
GIVEN: p = length of the longest side
Since the side lengths are
consecutive even integers, we can say:
p - 2 = length of the 2nd longest side
p - 4 = length of the shortest side
NOTE: The longest side is the HYPOTENUSE.
So, p = length of the HYPOTENUSE
And p - 2 = length of one leg of the right triangle
And p - 4 = length of the other leg of the right triangle
By the Pythagorean Theorem, we can write: (p - 2)² + (p - 4)² = p²
Check the answers . . . not there! Looks like we need to fiddle with the equation to make it look like on of the answer choices.
Take: (p - 2)² + (p - 4)² = p²
Subtract (p - 2)² from both sides to get: (p - 4)² = p² - (p - 2)² . . . BINGO!!
Answer: A
Cheers,
Brent
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