# In a right angled triangle, the sides forming the right angle differ by 7 cm. Find its sides, if its perimeter is 40cm.

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by amritKalita

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by amritKalita

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So, by pythagoras theorem,

1089+4x²-132x=x²+x²+49+14x

2x²+1040-146x=0

x²+520-73x=0

x²-73x+520=0

x²-8x-65x+520=0

x(x-8)-65(x-8)=0

(x-8)(x-65)=0

x-8=0 or x-65=0

therefore, x=8 or x=65

x={8,65}

If x=8

the sides are 8,15,17 cm.

If x=65

the sides are 65,72,-137 cm.