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Vlad1618 [11]
2 years ago
13

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.
Mathematics
1 answer:
snow_lady [41]2 years ago
6 0

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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