Question

Find the value of x.

Answer 1

Explanation:

To solve for x, you need the formula for the geometric means for similar right triangles. The big triangle is a right triangle; therefore, it is similar by definition, to the other right triangle. The 2 right triangles have the same hypotenuse, x. So we use the hypotenuse to find the value of x.

`(12)/(x)=(x)/(16)`

This gives us, by cross multiplication,

`x^2=12(16)` and

`x^2=192` so

x =
`√(192)` or
`8√(3)`