Question

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

Answer 1

From the information provided we will have the following:

$\begin{gathered} (x+9)^2=(x)^2+(x+7)^2\Rightarrow x^2+18x+81=x^2+x^2+14x+49 \\ \\ \Rightarrow x^2-4x-32=0\Rightarrow x=\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-32)}}{2(1)} \\ \\ \Rightarrow x=-4 \\ \\ and \\ \\ \Rightarrow x=8 \end{gathered}$

So, the lengths of the triangle are respectively:

$\begin{gathered} L=15 \\ \\ l=8 \\ \\ h=17 \end{gathered}$

So, the lengths are approximately 15 inches, 8inches and the hypotenuse is 17 inches.