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Question

# The length of one of the legs of a right angled triangle exceeds of the other leg by 10 cm but is smaller than that of the hypotenuse by 10 cm. Then the length of hypotenuse is:

A
50 cm
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B
80 cm
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C
70 cm
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D
none
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Solution

## The correct option is A 50 cmIn ΔABC,∠B=90°⇒Ac=hypotenuseAB&BC are two legs.Let AB>ACGiven one leg exceeds the other by 10cm∴AB=10+BCLet AB be xcm∴BC=(x−10)cm,AC=(10+x)cmAB2+BC2=AC2 (Pythagoras theorem)∴x2+(x−10)2=(10+x)2∴x2+x2+102−20x=102+x2+20x∴ length of hypotenuse=AC=(x+10)=50cm

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