The perimeter of a certain isosceles right triangle is 16 + 16√2. What is the length of the hypotenuse?
a. 8
b. 16
c. 4√2
d. 8√2
e. 16√2
The sides of an isosceles right triangle are in the following ratio: s : s : s√2.
Thus:
If s=side and h=hypotenuse, then h = s√2 and s = h/√2.
We can PLUG IN THE ANSWERS, which represent the length of the hypotenuse.
Because h = s√2, the average test-taker will assume that the correct answer must include √2.
Don't be an average test-taker.
Start with an answer choice that does NOT include √2.
Answer choice B: h = 16
In this case:
s = 16/√2 = (16*√2)/(√2*√2) = (16√2)/2 = 8√2.
Thus:
p = 8√2 + 8√2 + 16 = 16 + 16√2.
Success!
The correct answer is
B.
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