Question

Select the correct answer. what is the value of x in the triangle? an isosceles right triangle with two legs of length 10 and hypotenuse of length x a. b. c. d. e.

Answer 1

`10√(2)`

Step-by-step explanation:

There is a diagram attached which models the situation.

Since the given triangle is right, we are able to use the Pythagorean Theorem, which states when a and b are the legs of a right triangle and c is the hypotenuse:

`a^(2) + b^(2) = c^(2)`

We can plug in the given values. Since both legs have a value of ten, we can say:

`10^(2) + 10^(2) = c^(2)\\100 + 100 = c^(2)\\200 = c^(2)\\c = √(200)`

We can split 200 into 100 x 2, and
`√(100 )` is 10, so
`√(200) = 10√(2)`

Another way to do this use the given of the triangle being isosceles right. In an isosceles right triangle, the hypotenuse is always
`√(2)` times the base. So a triangle with legs 10 would have a hypotenuse of
`10√(2)`.