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Question

# If the hypotenuse of a right-angled triangle is 10 inches, and one leg of the triangle exceeds the other by 2 inches, then the shorter leg measures .

A
4 inches
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B
2 inches
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C
8 inches
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D
6 inches
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Solution

## The correct option is D 6 inchesLet the lengths of the shorter and longer legs of the right-angled triangle be x and x+2 inches respectively. Applying Pythagoras' theorem, we have x2+(x+2)2=102. ⟹x2+x2+4x+4=100 2x2+4x−96=0 ⇒x2+2x−48=0 i.e., x2+8x−6x−48=0 ⇒x(x+8)−6(x+8)=0 ⇒(x+8)(x−6)=0 Thus, the roots of the equation are 6 and -8. Since length cannot be negative, we have the shorter side of the triangle to be equal to x=6 inches.

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