Question

In a right triangle, the hypotenuse is $6m$ more than twice the shortest side. If the third side is $2m$ less than the hypotenuse. Then the length of the hypotenuse is

• A. 22
• B. 24
• C. 26
• D. 28

Answer 1

The correct option is C

26

Let $x$ be the shortest side

So, hypotenuse $=2x+6$

Third side $=2x+4$

Applying Pythagoras Theorem in the triangle,

$x^2+(2x+4{)}^2=(2x+6{)}^2$

$x^2+4x^2+16x+16=4x^2+24x+36$

$\Rightarrow 5x^2+16x+16=4x^2+24x+36$

$\Rightarrow x^2+16x+16=24x+36$

$\Rightarrow x^2-8x+16=36$

$\Rightarrow x^2-8x-20=0$

$\Rightarrow (x-10)(x+2)=0$

$\Rightarrow x=-2,10$

Ignoring the negative solution

$x=10m$

So, shortest side $=10m$

Hypotenuse $=2x+6=2\times 10+6=20+6=26m$