Question

the area if a playground is 238 yd ^2 the width of the playground is 3 yd longer than its length draw and label a diagram for the playground, write an equation that could be used to find x, the length of the playground, find the length and width of the play ground

Answer 1

Part a) The draw in the attached figure

Part b) The length of the playground is
`14\ yd` and the width of the playground is
`17\ yd`

Explanation:

I assume that the playground has a rectangular form

Let

x-----> the length of the playground

y ----> the width of the playground

we know that

The area of the playground is equal to

`A=xy`

`A=238\ yd^(2)`

so

`238=xy` -----> equation A

`y=x+3` -----> equation B

substitute equation B in equation A

`238=x(x+3)`

`x^(2) +3x=238`

`x^(2) +3x-238=0`

using a graphing calculator ------> solve the quadratic equation

The solution is

`x=14\ yd`

Find the value of y

`y=14+3=17\ yd`

therefore

The draw in the attached figure

The length of the playground is
`14\ yd`

The width of the playground is
`17\ yd`