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

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**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

Hence, , thus proved.

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