    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 hypotenuse is ___ m .

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 length of the shortest side. Then, by question, hypotenuse and the third side measure 2x+6 m and (2x+6)−2=2x+4 m respectively. Using Pythagoras' theorem, we have x2+(2x+4)2=(2x+6)2. ⇒x2+4x2+16x+16=4x2+24x+365x2+16x+16=4x2+24x+36x2−8x−20=0(x−10)(x+2)=0x=−2,10 Ignoring the negative solution as length of a side cannot be negative, we have x = 10 m (shortest side). Hypotenuse, 2x+6=2(10)+6=20+6=26 m.  Suggest Corrections  0      Similar questions  Related Videos   Pythogoras Theorem
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