A rectangular garden must have a perimeter of 155 feet and an area of at least 1400 square feet. Describe the possible lengths o
f the garden. Round your answers to the nearest foot. The approximate length of the garden is at least feet and at most feet.
1 answer:
Answer:
Step-by-step explanation:
Perimeter of a garden = 2(L+W)
Area of the gerden = LW
L is the length
W is the width
Given
Perimeter = 155ft
Area = 1400ft²
Substitute
1400 = LW
155 = 2L+2W
from 1;
W = 1400/L
Substitute into 2;
155 = 2L + 2(1400/L)
155 = 2L + 2800/L
155L = 2L² + 2800
2L²-155L + 2800 = 0
Factorize
L = 155±√155²-4(2)(2800)/4
L = 155±√24025-22400/4
L = 155±√1625/4
L = L = 155±40.31/4
L = 194.31/4
L = 48.82 feet and;
L = 155-40.31/4
L = 28.67ft
Hence the approximate length of the garden is at least 28.67 feet and at most 48.82 feet.
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