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

Answer:

Step-by-step explanation:

It is given that AB=a, BC=b, AC=c and BE=x.

Also, ABC is a right angled triangle, which is right angled at B and BE⊥AC.

From ΔABC and ΔAEB, we have

∠ABC=∠AEB=90°

∠BAC=∠EAB(Common)

Thus, By AA similarity,

ΔABC is similar to ΔAEB.

Therefore, using the similarity condition, we have

AC/AB = BC/EB

c/a=b/x

cx=ab

hence , ab=cx

thus proved..

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