Bluebook Math Question (Medium Level)

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1

<p>The lengths of the sides of a right triangle are consecutive even integers, and the length of the shortest side is x. Which of the following equations could be used to find x?</p>

<p>a. x + x + 1 = x +2
b. x^2 + (x+1)^2 = (x+2)^2
c. x^2 + (x+2)^2 = (x+4)^2
d. x + x + 2 = x + 4
e. x^2 = (x+2)(x+4)</p>

<p>The answer is C on page 491 of the Bluebook. Can anyone explain why this is so? Thanks a ton! This is the only question I actually missed (I left two blank, missed one, and got 13 right).</p>

2

<p>you know that in a right triangle a^2 + b^2 = c^2.</p>

<p>it is consecutive even integers so the three lengths will be x, x+2, and x+4.</p>

<p>then you just use pythagorean theorem, x^2 + (x+2)^2 = (x+4)^2</p>

3

<p>agreed with satsux</p>

4

<p>Another way to look at it would be to pick numbers. For example, I picked 6,8,10 and plugged in 6 for x. </p>

<p>a) 13 = 14 (wrong)
b) 85 = 64 (wrong)
c) 100 = 100 (right) --> You got the answer but lets just check
d) 14 = 10 (wrong)
e) 36 = 80 (wrong)</p>

<p>Therefore C is the only choice which works.</p>

5

<p>Thanks a lot, guys. Very helpful.</p>