Question

In the right triangle below, an altitude is drawn to the hypotenuse. Solve for x.

Can someone please explain this step by step?

Answer 1

x = 3√7

Explanation:

From the right triangle given in the picture,

Altitude or height of the triangle (AD) = x

Base or hypotenuse of the given triangle (BC) = 16

Length of segment BD = 16 - 7 = 9

By using geometric mean theorem in the given triangle,

`(AD)/(BD)=(DC)/(AD)`

(AD)² = (BD)(CD)

x² = 9×7

x = √63

x = 3√7