Question

Bill's new porch is rectangular, with an area of $50\mathrm{sq}.\mathrm{ft}$.

If the length of the porch is two times the width, what is the perimeter of the porch?

Answer 1

Finding the perimeter of the porch:

Given, the area of the porch is $50\mathrm{sq}.\mathrm{ft}$

Let the width be $x$, then the length will be $2x$

Now, we can write

$\begin{array}{rcl}\mathrm{Area}\mathrm{of}\mathrm{rectangle}& =& \mathrm{length}\times \mathrm{width}\\ & \Rightarrow & 50=2\mathrm{x}\times \mathrm{x}\\ & \Rightarrow & 25={\mathrm{x}}^2\\ & \Rightarrow & \mathrm{x}=5\end{array}$

Therefore, the sides of the rectangle are $10\mathrm{feet}\mathrm{and}5\mathrm{feet}$.

$\begin{array}{rcl}\mathrm{Perimeter}\mathrm{of}\mathrm{rectangle}& =& \mathrm{l}+w\\ & =& 10+5\\ & =& 15\mathrm{feet}\end{array}$

Hence, the perimeter of the rectangle is $15\mathrm{feet}$.