Question

The hypotenuse of a right angled triangle is $2$ centimeters more than the longer of the side containing the right angle. The shorter of the side containing the right angle is $7$ centimeters less than the longer side containing the right angle. Find the length of the hypotenuse.

Answer 1

Since the hypotenuse of a right triangle is $2cm$ more than the longer side of the triangle and the shorter side of the triangle is $7cm$ less than the longer side,

therefore, the hypotenuse $=x+9$, one side $=x$ and the other side $=x+7$.
From here, you apply Pythagorean theorem:
$a^2+b^2=c^2$
where
$c$ is length of hypotenuse
$a$ and $b$ are the lengths of the two sides
.
$x^2+(x+7{)}^2=(x+9{)}^2$
$x^2+(x+7)(x+7)=(x+9)(x+9)$
$x^2+(x^2+14x+49)=(x^2+18x+81)$
$2x^2+14x+49=x^2+18x+81$
$x^2-4x-32=0$

Factoring:

$(x-8)(x+4)=0$
$x=-4,8$

We can throw out the negative solution leaving:
$x=8cm$ (short legth)

long legth $=x+7=8+7=15cm$

hypotenuse $=x+9=8+9=17cm$

Hence, the length of the hypotenuse is $17cm$.