Question

The length of a rectangle is $12$ cm more than the width. The perimeter is $74$ cm. Find the length and the width.

Short answer

The length and the width of the given rectangle is $24.5cm$and $12.5cm$.

Step-by-step solution

Step 1. Given information.

Consider the given question,

Perimeter of the given rectangle is $74cm$.

Step 2. Find the length and breadth.

Assume w and lto be the width and length of the rectangle. Then,

$l=w+12$

We know the formula of the perimeter of the rectangle is given below,

$$\begin{gathered} P=2\left(l+w\right)......\left(i\right) \\ 74=2\left\{w+\left(w+12\right)\right\} \\ 37=2w+12 \\ w=12.5cm \end{gathered}$$

Then,

$$\begin{gathered} l=12.5+12 \\ l=24.5cm \end{gathered}$$

Step 3. Check the answer.

Substitute the values of length and width in equation (i),

$$\begin{gathered} P=2\left(24.5+12.5\right) \\ P=2\left(37\right) \\ P=74cm \end{gathered}$$

Hence, the values of the length and width obtained is correct.