Question

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

Answer 1

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Answer 2

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

$\frac{AC}{AB}=\frac{BC}{EB}$

$\frac{c}{a}=\frac{b}{x}$

$cx=ab$

Hence, $ab=cx$, thus proved.