Answer
Short leg: $17.6$ inches
Long leg: $18.6$ inches
Hypotenuse: $25.6$ inches
Work Step by Step
Let's note:
$s$=the shorter leg
$l$=the longer leg
$h$=the hypotenuse
We are given:
$$\begin{align*}
l&=s+1\\
h&=l+7\
\end{align*}$$
Rewrite $h$ in terms of $s$:
$$h=l+7=s+1+7=s+8.$$
Use the Pythagorean theorem:
$$\begin{align*}
h^2&=s^2+l^2\\
(s+8)^2&=s^2+(s+1)^2\\
s^2+16s+64&=s^2+s^2+2s+1\\
0&=2s^2+2s+1-s^2-16s-64\\
0&=s^2-14s-63.
\end{align*}$$
Solve the equation using the Quadratic Formula:
$$\begin{align*}
s^2-14s-63&=0\\
s&=\dfrac{-(-14)\pm\sqrt{(-14)^2-4(1)(-63)}}{2(1)}\\
&=\dfrac{14\pm 21.17}{2}\\
s_1&\approx -3.6\\
s_2&\approx 17.6.
\end{align*}$$
As $s>0$, the only solution is $s=17.6$.
Determine $l$ and $h$:
$$\begin{align*}
l&=s+1=17.6+1=18.6\\
h&=s+8=17.6+8=25.6\
\end{align*}$$
