Question

The shorter leg of a right triangle 9cm is shorter than the longer leg. The hypotenuse is 9cm longer than the longer leg. Find the side lengths of the triangle.

Answer 1

Answer:

Shorter leg: 27 cm,

Longer leg: 36 cm,

Hypotenuse: 45 cm.

Step-by-step explanation:

Let x represent longer leg of the triangle.

We have been given that the shorter leg of a right triangle 9 cm is shorter than the longer leg. This means that the shorter leg of right triangle would be $x-9$ cm.

We are told that hypotenuse is 9 cm longer than the longer leg.This means that the hypotenuse of right triangle would be $x+9$ cm.

Now, we will use Pythagoras theorem to solve for x as:

$x^2+(x-9)^2=(x+9)^2$

$x^2+x^2-18x+81=x^2+18x+81$

Upon simplifying our equation, we will get:

$x^2-18x=18x$

$x^2-18x-18x=18x-18x$

$x^2-36x=0$

$x(x-36)=0$

Using zero product property, we will get:

$x=0\text{ (or) }(x-36)=0$

$x=0\text{ (or) }x=36$

Since longer side of a right triangle cannot be 0, therefore, longer side of the right triangle is 36 cm.

The shorter side of right triangle would be $x-9\Rightarrow 36-9=27$ cm. Therefore, the shorter side of the right triangle would be 27 cm.

The hypotenuse of right triangle would be $x+9\Rightarrow 36+9=45$ cm.Therefore, the hypotenuse of the right triangle would be 45 cm.