Question

Find the measure of X, Y and Z in simplest form:

Answer 1

Answer/Explanation:

`12^2 = 16*x` (altitude to hypotenuse theorem)

Solve for x using this equation

`144 = 16x`

`(144)/(16) = x` (division property of equality)

`9 = x`

`x = 9`

`y^2 = 12^2 + x^2` (pythagorean theorem)

`y^2 = 12^2 + 9^2` (substitution)

`y^2 = 144 + 81`

`y^2 = 225`

`√(y^2) = √(225)`

`y = 15`

`z^2 = (x + 16)^2 - y^2` (pythagorean theorem)

`z^2 = (9 + 16)^2 + 15^2` (substitution)

`z^2 = 25^2 + 15^2`

`z^2 = 625 + 225`

`z^2 = 850`

`√(z^2) = √(850)`

`z = √(25*34)`

`z = 5√(34)`