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The hypotenuse of a right triangle is 6 m more than the twice of the shortest side. If the third side is 2 m less than the hypotenuse, what is the area of the triangle? ​

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The hypotenuse of a right -...

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Asked on November 22, 2019 by

Chaya Panchal

The hypotenuse of a right-angled triangle is 6 meters more than twice the shortest side. If the third side is 2 meters less than the hypotenuse, find the sides of the triangle.

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ANSWER

Let the length of the shortest side be x meters.

Then, hypotenuse=(2x+6) metres

And the third side (2x+6−2) metre=(2x+4) metres

By Pythagoras theorem, we have

(2x+6)

2

=x

2

+(2x+4)

2

⇒x

2

−8x−20=0

⇒x

2

−10x−2x−20=0

⇒(x−10)(x+2)=0

⇒x=10orx=−2

∵ x can not be a negative $$\therefore

⇒x=10

Length of the shortest side =10 metres

Length of the hypotenuse =(2x+6) metres=26 metres

Length of the third side =(2x+4) metres=24 metres

Hence the sides of the triangle are 10m,26m and 24m