Bernie put in a garden in her back yard. The garden has a perimeter of 272 feet. She wants to know the total surface area of the garden and all she knows is the perimeter and that the width is 20% or (1/5) of the length. (Remember 20% and the fraction 1/5 is the same decimal value) Use a system of equations for finding the length and width so you can calculate the area. Your area answer does not need to include the unit as the answer assumes you will use feet2.
P = 2L + 2W
272 = 2L + 2(0.2L)
272 = 2.4L
272/2.4 = L
113.333 = L
To find the length and width of the garden, we can set up a system of equations based on the given information.
Let's assume the length of the garden is "L" and the width is "W."
We know the width is 20% or 1/5 of the length, so we can represent this as W = (1/5)L.
The perimeter of a rectangle is equal to twice the length plus twice the width, so we have the equation:
2L + 2W = 272.
Now, let's substitute the value of W from the first equation into the second equation:
2L + 2(1/5)L = 272.
2L + 2/5L = 272.
(10/5)L + (2/5)L = 272.
(12/5)L = 272.
To solve for L, we can multiply both sides of the equation by (5/12):
L = (272 * 5/12).
L = 113.
Now that we have the length, we can find the width by substituting the value of L into the equation W = (1/5)L:
W = (1/5) * 113.
W = 22.6.
The length of the garden is 113 feet, and the width is 22.6 feet.
To calculate the total surface area of the garden, we multiply the length and width:
Area = L * W.
Area = 113 * 22.6.
Area ≈ 2559.8 square feet.
Therefore, the total surface area of the garden is approximately 2559.8 square feet.