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Question

# In a right triangle, the hypotenuse is 6 m more than twice the shortest side. If the third side is 2 m less than the hypotenuse. Then the length of the hypotenuse is

A

22

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B

24

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C

26

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D

28

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Solution

## The correct option is C 26 Let x be the shortest side So, hypotenuse =2x+6 Third side =2x+4 Applying Pythagoras Theorem in the triangle, x2+(2x+4)2=(2x+6)2 x2+4x2+16x+16=4x2+24x+36 ⇒5x2+16x+16=4x2+24x+36 ⇒x2+16x+16=24x+36 ⇒x2−8x+16=36 ⇒x2−8x−20=0 ⇒(x−10)(x+2)=0 ⇒x=−2,10 Ignoring the negative solution x=10 m So, shortest side =10 m Hypotenuse =2x+6=2×10+6=20+6=26 m

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