Solve the following problems: a Given: △ABC, m∠B=90° AB=12, BC=16, BK ⊥ AC . Find: AC and BK.

Question

Given: △ABC, m∠B=90°

AB=12, BC=16,

BK

 ⊥

AC

 . 

    Find: AC and BK.

Answer 1

Let BK = h, AK = y and BK=x

AC=20 (this is a 3-4-5 right triangle)

h² + y² =144

h² + x² = 256

Subtract

x² - y² = 112

(x+y)(x-y)=112

x+y =20

Divide

x-y=5.6

x+y=20

2x =25.6

x=12.8

y=7.2