The perimeter of a certain isosceles right triangle is 16 + 16√2. What is the length of the hypoteneuse?
a. 8
b. 16
c. 4√2
d. 8√2
e. 16√2
OA is b.
Could someone please explain this answer?
thanks
The sides of an isosceles right triangle are proportioned: s : s : s√2.
So if s=side and h=hypotenuse, then h = s√2 and s = h/√2.
We can plug in the answers, which represent the hypotenuse.
Answer choice C: h = 4√2
s = (4√2)/√2 = 4.
p = 4 + 4 + 4√2 = 8 + 4√2.
Eliminate C. The perimeter needs to be quite a bit larger.
Answer choice B: h = 16
s = 16/√2 = (16*√2)/(√2*√2) = (16√2)/2 = 8√2.
p = 8√2 + 8√2 + 16 = 16 + 16√2. Success!
The correct answer is
B.
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