Question

The longer leg of a right triangle is 7 cm longer than the shorter leg. The hypotenuse is 9 cm longer than the shorter leg. Find the side lengths of the triangle.

Length of the shorter leg:

Length of the longer leg:

Lengthy of the hypotenuse:

Answer 1

Answer:

The length of the shorter leg=8 cm

length of the longer leg=8+7=15 cm

length of the hypotenuse=8+9=17 cm

Explanation:

Let the shorter leg=x cm

So, longer length=x+7 cm

So, hypotenuse=x+9 cm

For a right triangle, using pythagorous theorem.

longer length²+shorter length²=hypotenuse²

$(x+7)^2+x^2=(x+9)^2$

$x^2+7^2+2*7*x+x^2=x^2+9^2+2*9*x$

$x^2+49+14x+x^2=x^2+81+18x$

$2x^2+14x+49=x^2+18x+81$

Rearranging the like terms together.

$2x^2-x^2+14x-18x+49-81=0$

$x^2-4x-32=0$

Solving by factoring method

$x^2-8x+4x-32=0$

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

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

So, $(x-8)=0\Rightarrow x=8$ (Acceptable)

and $(x+4)=0\Rightarrow x=-4$ (NOT acceptable since, it is negative).

Hence,

The length of the shorter leg=8 cm

length of the longer leg=8+7=15 cm

length of the hypotenuse=8+9=17 cm