Question

# The length of the hypotenuse of a right angle triangle exceeds the length of the base by 2 cm and exceeds twice the length of the attitude by 1 cm. The perimeter of the triangle is:

A
18 cm
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B
17 cm
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C
25 cm
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D
40 cm
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Solution

## The correct option is D 40 cmLet length of the hypotenuse be x.length =x−12and breadth =x−2Applying Pythagoras theorem(x−2)2+(x−1)24=x2(x−1)24=x2−(x−2)2On solving, 16(x−1)=(x−1)2x2−2x+1=16x−16x2−18x+17=0(x−1)(x−17)=0Taking x=17, we get the rest as altitude =8cm Base =15cm∴ perimeter of triangle =17+8+15=40cm

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