Alex is building a rectangular fence around his yard. The total perimeter of the fence is 68 feet and the area of the yard is 24
0 square feet. Based on this information, what are the dimensions of the fence?
2 answers:
Perimeter (P) = 2L + 2w
68 = 2L + 2w
68 - 2L = 2w
2(34 - L) = 2(w)
34 - L = w
********************
Area (A) = L * w
240 = L (34 - L)
240 = 34L - L²
L² - 34L + 240 = 0
(L - 10)(L - 24) = 0
L = 10 or L = 24
w = 34 - L = 34 - 10 = 24 or w = 34 - 24 = 10
Answer: width = 10, length = 24 assuming length is bigger than the width
Perimeter (P) = 2L + 2w
68 = 2L + 2w
68 - 2L = 2w
2(34 - L) = 2(w)
34 - L = w
********************
Area (A) = L * w
240 = L (34 - L)
240 = 34L - L²
L² - 34L + 240 = 0
(L - 10)(L - 24) = 0
L = 10 or L = 24
w = 34 - L = 34 - 10 = 24 or w = 34 - 24 = 10
Answer: width = 10, length = 24 <em>assuming length is bigger than the width</em>
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