Question

The perimeter of the rectangle below is 112 units. Find the length of side BC.Write your answer without variables.4y+2 BC =

Answer 1

The perimeter of a rectangle is given by:

$P=2L+2W$

Where L is the length and W is the width.

By replacing the given information we have:

$112=2(5y)+2(4y+2)$

Now, we have to solve for y as follows:

$\begin{gathered} \text{Apply the distributive property} \\ 112=10y+2\cdot4y+2\cdot2 \\ 112=10y+8y+4 \\ 112=18y+4 \\ 112-4=18y \\ 108=18y \\ y=\frac{108}{18} \\ y=6 \end{gathered}$

Replace the y-value into the BC side expression and solve:

$\begin{gathered} BC=4y+2 \\ BC=4(6)+2 \\ BC=24+2 \\ BC=26 \end{gathered}$