Question

In a right triangle, the hypotenuse is $6\text{m}$ more than twice the shortest side. If the third side is $2\text{m}$ less than the hypotenuse, then the length of the hypotenuse is [in m]

• A. 22
• B. 24
• C. 26
• D. 28

Answer 1

The correct option is C

26

Let $x$ be the shortest side

then,
$2x+6$ is the hypotenuse
$2x+6-2=2x+4$ is the third side [given]

$\Rightarrow x^2+(2x+4{)}^2=(2x+6{)}^2$ [using Pythagoras Theorem]
$\Rightarrow x^2+(2x+4)(2x+4)=(2x+6)(2x+6)$

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

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

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

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

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

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

$\Rightarrow x=\{-2,10\}$

Ignoring the negative solution [which will result in the values of two sides as negative, which makes no sense]

$x=10\text{m}$ [short side]

hypotenuse $=2x+6=2\times 10+6=20+6=26\text{m}$