Answer
$20, 15$
Work Step by Step
Step 1. Assume the length is $x$ and the width is $y$.
Step 2. Based on the given conditions, set up the system of equations:
\begin{cases} 2(x+y)=70 \\ x^2+y^2=25^2\end{cases}
Step 3. The first equation gives: $y=35-x$, use it in the second equation to get:
$x^2+(35-x)^2=25^2$ or $2x^2-70x+35^2-25^2=0$ or $x^2-35x+300=0$
Step 4. Factor the above equation as $(x-20)(x-15)=0$ to get $x=15, 20$
Step 5. Consider $x$ is the length, we can get the answer as $x=20, y=15$
