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

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calculista calculista · Answer 1 · 2019-04-27T20:16:03+02:00

Answer:

Part a) The draw in the attached figure

Part b) The length of the playground is [tex]14\ yd[/tex] and the width of the playground is [tex]17\ yd[/tex]

Step-by-step 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

[tex]A=xy[/tex]

[tex]A=238\ yd^{2}[/tex]

so

[tex]238=xy[/tex] -----> equation A

[tex]y=x+3[/tex] -----> equation B

substitute equation B in equation A

[tex]238=x(x+3)[/tex]

[tex]x^{2} +3x=238[/tex]

[tex]x^{2} +3x-238=0[/tex]

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

The solution is

[tex]x=14\ yd[/tex]

Find the value of y

[tex]y=14+3=17\ yd[/tex]

therefore

The draw in the attached figure

The length of the playground is [tex]14\ yd[/tex]

The width of the playground is [tex]17\ yd[/tex]