gmattesttaker2 wrote:Hello,
Can you please assist with this:
A certain right triangle has integer sides; if the lengths of its sides are 11, y, and (y + 1), which of the following could be the value of y?
(A) 60
(B) 50
(C) 40
(D) 30
(E) 20
OA: A
Thanks,
Sri
The length of the longest side -- the hypotenuse -- must be the greatest of 11, y and y+1.
Since the answer choices -- which represent the value of y -- are all greater than 11, the length of the hypotenuse must be equal to y+1.
Applying the Pythagorean theorem, we get:
11² + y² = (y+1)²
(y+1)² - y² = 121.
We can plug in the answers for the value of y.
Remember the following identity:
a² - b² = (a+b)(a-b).
Answer choice C: y=40
41² - 40² = (41+40)(41-40) = 81.
The difference is TOO SMALL, implying that the value of y must be GREATER than 40.
Eliminate C, D and E.
Answer choice B: y=50
51² - 50² = (51+50)(51-50) = 101.
The difference is still too small.
Eliminate B.
The correct answer is
A.
Answer choice
A: y=60
61² - 60² = (61+60)(61-60) = 121.
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