Question

ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC. Prove that :

If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.

Answer 1

Since ΔADE ~ ΔACB, their sides are proportional

`=> (AE)/(AB) = (AD)/(AC) = (DE)/(BC)` ....(1)

In ΔABC, by Pythagoras Theorem, we have

`AB^2 + BC^2 = AC^2`

`=> AB^2 + 5^2 = 13^2`

`=> AB = 12 cm`

From equation 1 we have

`4/12 = (AD)/13 = (DE)/5`

`=> 52/12= (AD)`

`=> AD = 4 1/3cm`

Also `4/12 = (DE)/5`

`=> DE  = 20/12 = 5/3 = 1 2/3 cm`