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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.
Solution
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"AC"/"CD"="AB"/"CB"` [Corresponding parts of similar Δ are proportional]
`rArrb/x=c/a`
⇒ ab = cx
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