amirhakimi wrote:The Perimeter of a certain isosceles right triangle is 16 + 16√2. What is the length of the hypotenuse of the triangle?
A)8
B)16
C)4√2
D)8√2
E)16√2
Answer is B
Another option is to test the answer choices.
We'll use the fact that, for any isosceles right triangle, the sides have length x, x, and x√2 for some positive value of x.
The hypotenuse is x√2
So, if x is the length of one leg of the right triangle, the perimeter = x + x + x√2
Start with
answer choice D.
If the hypotenuse is 8√2, then x = 8
[since the hypotenuse = x√2]
So, the perimeter = 8 + 8 + 8√2 = 16 + 8√2
NO GOOD! We're told that the perimeter is 16 + 16√2, so we need the triangle to be LARGER THAN 8√2.
This means we can ELIMINATE A, C and D
IMPORTANT: At this point, we can test either B or E. It doesn't matter which one we test. If B works, we're done. If B doesn't work, then we'll automatically choose E.
Let's try
answer choice B.
If the hypotenuse is 16, then we know that x√2 = 16
So, x = 16/√2 = 8√2
So, in this instance, the perimeter is 8√2 + 8√2 + 16 = 16√2 + 16
PERFECT! We're told that the perimeter is 16 + 16√2
Answer:
B
Cheers,
Brent
