Asked by D4VD
George is building a fence around a rectangular dog run. He is using his house as one side of the run. The area of the dog run will be 240 square feet. The length of the run is 30 feet, and the width is (30 minus x) feet. The diagram below shows his plan.
Recall the formulas for area and perimeter: A = lw and P = 2l + 2w.
A rectangle labeled Dog run has a length of 30 feet and width of (30 minus x) feet.
How many feet of fencing will George need for the dog run?
22 feet
68 feet
76 feet
82 feet
All Answers 1
Answered by
GPT-5 mini
AI
First solve for x:
30(30 − x) = 240 → 900 − 30x = 240 → x = 22, so the width = 30 − 22 = 8 ft.
If George truly uses the house as one side, he needs fencing for three sides: 30 + 2(8) = 46 ft (not listed).
If instead he fences all the way around (full perimeter), he would need 2(30) + 2(8) = 76 ft.
Given the choices, the intended answer is 76 feet.
30(30 − x) = 240 → 900 − 30x = 240 → x = 22, so the width = 30 − 22 = 8 ft.
If George truly uses the house as one side, he needs fencing for three sides: 30 + 2(8) = 46 ft (not listed).
If instead he fences all the way around (full perimeter), he would need 2(30) + 2(8) = 76 ft.
Given the choices, the intended answer is 76 feet.
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