Answer:
See Explanation
Step-by-step explanation:
Your question do not have enough details for it to be answered. I will solve your question on a general terms using the attached image of a trapezoid
Given
[tex]Area = 8580ft^2[/tex]
From the attachment, we have:
[tex]BC = 100ft[/tex]
[tex]AD = 80ft[/tex]
[tex]h = 60ft[/tex] --- height
The perimeter (P) of a trapezoid is:
[tex]P = AB + BC + CD + AD[/tex]
Substitute values for AD, BC
[tex]P = AB + 100 + CD + 80[/tex]
Collect Like Terms
[tex]P = AB + CD + 80+ 100[/tex]
[tex]P = AB + CD + 180[/tex]
Next, is to calculate the lengths of AB and CD or the sum: AB + CD
The area of a trapezoid is:
[tex]Area = \frac{1}{2}(AB + CD) * h[/tex]
Substitute values for Area and h
[tex]8580= \frac{1}{2}(AB + CD) * 60[/tex]
Multiply both sides by 2
[tex]2*8580= \frac{1}{2}(AB + CD) * 60*2[/tex]
[tex]17160= (AB + CD) * 60[/tex]
Divide both sides by 60
[tex]\frac{17160}{60}= \frac{(AB + CD) * 60}{60}[/tex]
[tex]286 = AB + CD[/tex]
[tex]AB + CD=286[/tex]
Substitute 286 for AB + CD in: [tex]P = AB + CD + 180[/tex]
[tex]P = 286 + 180[/tex]
[tex]P = 466[/tex]
The perimeter of the backyard is 466ft.
The above steps should give you a hint on how to solve your actual question.
