Question

The area of a playground is 154 yd ^2. The width of the playground is 3 yd longer than its length. FInd the length and width of the playground.

Answer 1

The length of the playground = 11 yards

The width of the playground = 14 yards

Step-by-step explanation:

Let the length of the playground = l yd.

The width of the playground is 3 yd longer than its length.

Therefore, the width of the playground = (l+3) yd

Area of a Rectangle = Length x Width

Substituting the given values, we have:

`154=l(l+3)`

We then solve the equation above for l.

`l^2+3l-154=0`

We factorize:

`\begin{gathered} l^2+14l-11l-154=0 \\ l(l+14)-11(l+14)=0 \\ (l-11)(l+14)=0 \\ l-11=0\text{ or l+14=0} \\ l=11\text{ yards, }l\\eq-14 \end{gathered}`

The length of the playground = 11 yards

The width of the playground = 14 yards