Kayla designed a rectangular patio that was 3 times as long as it was wide and had a perimeter of 160 feet. What was the area of the patio?
If x = width, then 3x = length.
2x + 2(3x) = 160
Solve for x and 3x.
Insert in equation below.
x * 3x = area
To find the area of the patio, we need to know the dimensions of the rectangle.
Let's let the width of the patio be "x" feet.
According to the problem, the length of the patio is 3 times as long as it is wide, so the length would be 3x feet.
The formula for the perimeter of a rectangle is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
Given that the perimeter of the patio is 160 feet, we can set up the equation:
160 = 2(3x) + 2x
Simplifying the equation:
160 = 6x + 2x
160 = 8x
Dividing both sides of the equation by 8:
20 = x
So, the width of the patio is 20 feet.
Now that we know the width, we can find the length:
Length = 3x = 3 * 20 = 60 feet
The area of a rectangle is given by the formula A = L * W, where A is the area, L is the length, and W is the width.
Plugging in the values we found:
Area = 60 * 20 = 1200 square feet
Therefore, the area of the patio is 1200 square feet.