Answer: 51.86 and 23.14
Step-by-step explanation:
The rectangular garden must have a perimeter of 150 feet
Perimeter of rectangular garden =
2l + 2w=150 -----------1
The rectangular garden must have a perimeter of 150 feet and an area of at least 1200 square feet.
Area of rectangular garden =
l×w= 1200 feet^2 -----------2
From equation 2, l=1200/w
Put l=1200/w in equation 1
2× 1200/w + 2w = 150
(2400/w) +2w = 150
(2400+2w^2)/w =150
2400+2w^2= 150w
2w^2- 150w+2400=0
Using the general formula
w = [-b+-√(b^2-4ac)]/2a
a = 2, b =-150, c=2400
w =[--150+/-√(-150^2-4×2×2400)]/2×2
=[150+/-√(22500-19200)]/4
=[150+/-√3300)]/4
=(150+57.45)/4 or (150-57.45)/4
w= 207.45/4 or 92.55/4
w= 51.86 or w= 23.14
l = 1200/51.86 or l= 1200/23.14
l = 23.14. or l= 51.86
For an area of at least 1200ft^2
The dimensions are 51.86 and 23.14
The length of the garden is: l ≤ 23 ft or l ≥ 52ft
Let the length of the garden be represented by l
Let the width of the garden be represented by w
Perimeter, P = 150 feet
The perimeter of the rectangle = 2(l + w)
2(l + w) = 150
l + w = 75......................(1)
The area of the rectangle(A) = Length x width
A = lw
lw ≤ 1200...........(2)
Make w the subject of the formula in equation (1)
w = 75 - l...............(3)
Substitute equation (3) into equation (2)
(75 - l)(l) ≤ 1200
75l - l² ≤ 1200
0 ≤ l² - 75l + 1200
l² - 75l + 1200 ≥ 0
Solving the quadratic inequality above:
l ≥ 51.86 or l ≤ 23.13
Therefore, the length of the garden is: l ≤ 23 ft or l ≥ 52
Learn more here: https://brainly.com/question/18268775
