Question

Find the value of x.

Answer 1

x = 10

Explanation:

Look at the picture.

Use the Pythagorean theorem to calculate y:

`y^2+8^2=12^2`

`y^2+64=144` subtract 64 from both sides

`y^2=80\to y=√(80)`

Two smaller triangles are similar. Therefore the sides are in proportion:

`(x)/(y)=(y)/(8)` cross multiply

`y^2=8x` substitute y² = 80

`80=8x` divide both sides by 8

`x=10`