Bernie put in a garden in her back yard. The garden has a perimeter of 195 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.
Here's a similar problem and solution.
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To find the length and width of the garden, we can set up a system of equations using the given information.
Let's denote the length of the garden as L and the width as W.
We are given that the width is 20% or 1/5 of the length, which can be expressed as:
W = (1/5)L
The perimeter of a rectangle is equal to the sum of all its sides. In this case, the perimeter of the garden is given as 195 feet, so we can write the equation:
2L + 2W = 195
Now we can substitute the value of W from the first equation into the second equation:
2L + 2(1/5)L = 195
Simplifying this equation, we get:
2L + (2/5)L = 195
(10/5)L + (2/5)L = 195
(12/5)L = 195
To isolate L, we can multiply both sides of the equation by the reciprocal of (12/5), which is (5/12):
(5/12)(12/5)L = (5/12)(195)
L = 975/12
L ≈ 81.25 feet
Now we can substitute this value back into the first equation to find the width:
W = (1/5)(81.25)
W ≈ 16.25 feet
To calculate the total surface area of the garden, we multiply the length and width:
Area = L * W
Area = (81.25)(16.25)
Area ≈ 1320.31 square feet
Therefore, the total surface area of the garden is approximately 1320.31 square feet.