Q. 54.3( 13 Votes )

In a right angled

Answer :

Given: In a right angled triangle with sides a and b and hypotenuse c, the altitude drawn on the hypotenuse is x.

To prove: ab = cx

Proof:

Let in a right-angled triangle ABC at B, a perpendicular from C to AB is drawn such that
BC = a
AC = b
BA = c
BD = x


In ΔABC and ΔCDB


∠B = ∠B (Common)


ABC = CDB (Both 90°)


Then, ΔABC ~ ΔCDB (By AA Similarity)


So, (Corresponding parts of similar triangle area proportion)


Or


Or ab = cx

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