Question

Finding the side length of a rectangle given its perimeter or areaThe perimeter of a rectangular painting is 354 centimeters. If the width of the painting is 81 centimeters, what is its length?centimeters?

Answer 1

The perimeter of a reactangle is calculated using the formula

$P=2(L+W)$

Where

P = perimeter

L = length

W = width

Given:

$\begin{gathered} P=354\operatorname{cm} \\ W=81\operatorname{cm} \end{gathered}$

Substitute these values into the formula

$354=2(L+81)$

Divide both sides by 2

$\begin{gathered} \frac{354}{2}=\frac{2(L+81)}{2} \\ 177=L+81 \end{gathered}$

Substract 81 from both sides

$\begin{gathered} 117-81=L+81-81 \\ L=96 \end{gathered}$

Therefore, the length of the rectangle is 96 centimeters