Question

In a right angled triangle with sides a and b and hypotenuse c, the altitude drawn on the hypotenuse is x. Prove that ab = cx.

Answer 1

We have: ∠C = 90° and CD ⊥ AB

In ΔACB and ΔCDB

∠B = ∠B [common]

∠ACB = ∠CDB [Each 90°]

Then, ΔACB ~ ΔCDB [By AA similarity]

`therefore"AB"/"BD"="AC"/"BC"`      [Corresponding parts of similar Δ are proportional]

`rArra/x=c/b`

⇒ ab = cx