Question

Find the length of a rectangle with: perimeter 30 and width 6.

Short answer

The length of the rectangle is 9.

Step-by-step solution

Step 1. Given information

The perimeter of the rectangle is, $P=30$.

The width of the rectangle is, $w=6$.

We need to find the length, l of the rectangle.

Step 2. Use the formula for the perimeter of the rectangle.

The perimeter of the rectangle is, $P=2(l+w)$.

We get

$$\begin{gathered} \frac{P}{2}=l+w \\ \frac{P}{2}-w=l \\ l=\frac{P}{2}-w \end{gathered}$$

Step 3. Substitute the values in l=P2-w.

We get

$$\begin{gathered} l=\frac{30}{2}-6 \\ =15-6 \\ =9 \end{gathered}$$

The length of the rectangle is 9.