Bernie put in a garden in her back yard. The garden has a perimeter of 265 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 solve this problem, 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 that the width is 20% or 1/5 of the length, so we can write the equation:
W = (1/5)L
The perimeter of a rectangle can be calculated by adding up all the sides, so we have:
2L + 2W = 265
Now we have a system of equations with two variables. We can solve this system to find the values of L and W, which will allow us to calculate the area.
To solve the system of equations, we can use substitution or elimination. Let's use substitution in this case.
We'll start by rearranging the first equation to solve for L:
W = (1/5)L
Multiply both sides by 5 to eliminate the fraction:
5W = L
Now we can substitute this value of L into the second equation:
2L + 2W = 265
2(5W) + 2W = 265
10W + 2W = 265
12W = 265
Divide both sides by 12 to solve for W:
W = 265/12
W ≈ 22.08
Now we can substitute this value of W back into the first equation to solve for L:
5W = L
5(22.08) = L
L ≈ 110.40
So, the length of the garden is approximately 110.40 feet, and the width is approximately 22.08 feet.
To calculate the area of the garden, we can multiply the length and width:
Area = Length × Width
Area ≈ 110.40 × 22.08
Area ≈ 2440.35 square feet
Therefore, the total surface area of the garden is approximately 2440.35 square feet.