Answer
$l= r^2 +5r+1$.
Work Step by Step
Length of the rectangle $=l$.
Width of the rectangle $w=r-5$
Area of the rectangle is $A=Length \times width$
Substitute both values.
$A=l\times (r-5)$
$A=r^3-24r-5$.
Equate both values.
$\Rightarrow l\times (r-5)=r^3-24r-5$
Divide both sides by $r-5$.
$\Rightarrow l=\frac{r^3-24r-5}{r-5}$
$(r^3-24r-5)\div(r-5)$
Rewrite the expression in standard form.
$(r^3+0r^2-24r-5)\div(r-5)$
$\begin{matrix}
& r^2 & +5r &+1 & & \leftarrow &Quotient\\
&-- &-- &--&--& \\
r-5) &r^3&+0r^2&-24r&-5 & \\
& r^3 & -5r^2 & & & \leftarrow &r^2(r-5) \\
& -- & -- & & & \leftarrow &subtract \\
& 0 & +5r^2 & -24r & & \\
& & 5r^2 & -25r & & \leftarrow & 5r(r-5) \\
& & -- & -- & & \leftarrow & subtract \\
& & 0&r &-5& \\
& & & r& -5 & \leftarrow & 1(r-5) \\
& & & -- & -- & \leftarrow & subtract \\
& & & 0 & 0 & \leftarrow & Remainder
\end{matrix}$
The answer is
$\Rightarrow Quotient + \frac{Remainder}{Divisor}$
$\Rightarrow r^2 +5r+1+\frac{0}{r-5}$
Simplify.
$\Rightarrow r^2 +5r+1$.
