32.8k views
5 votes
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

User Calimo
by
7.3k points

1 Answer

4 votes

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=(-(-4)\pm√((-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.

User Jander
by
6.9k points