From the GMAT online practice test

[marie]

I can't figure this one, I suspect maybe the answer is wrong?

Q: The perimeter of a certain isosceles right triangle is 16 + 16sqrt(2). What is the length of the hypotenuse of the triangle?

- 8
- 16
- 4 sqrt(2)
- 8sqrt(2)
- 16sqrt(2)

The answer says 16, but I think the question should have read the perimeter is 32 + 16sqrt(2). Any thoughts?

[mschling52]

I think 16 is the right answer.

Let x be the length of the hypotenuse. Then, since we are dealing with a 45-45-90 triangle, the lengths of the other 2 sides are each (x/sqrt(2)).

So, the perimeter of the triangle will be x+(2x)/sqrt(2). We are given the perimeter, so we can set this equation equal to 16+16sqrt(2) and solve for x.

x+(2x)/sqrt(2) = 16+16sqrt(2)

x(1+2/sqrt(2)) = 16(1+sqrt(2))

x(1+sqrt(2)) = 16(1+sqrt(2))

x=16

To double check, the perimeter of a 45-45-90 triangle with hypotenuse of 16 will be

16+16/sqrt(2)+16/sqrt(2) = 16+32/sqrt(2) = 16+(32sqrt(2))/2
= 16 + 16sqrt(2),

which matches the perimeter given in the question

[marie]

Thanks I can see that, so simple, great expanation.