Suppose that the perimeter of a rectangle is 48 ft and the length is thrice the width. What are the idmensions of this rectangle and what is the area?
P = Perimeter
L = Length
W = Width
P = 2 W + 2 L = 2 ( W + L )
L = 2 W
P = 2 ( W + L ) = 2 ( W + 2 W ) = 2 * 3 W = 6 W
48 = 6 W Divide both sides by 6
48 / 6 = 6 W / 6
8 = W
W = 8 ft
L = 2 W = 2 * 8 = 16 ft
P = 2 ( W + L ) = 2 ( 8 + 16 ) = 2 * 24 = 48 ft
A = W * L = 8 * 16 = 128 ft ^ 2
To find the dimensions and area of this rectangle, we can use the information given. Let's start by assigning variables to the unknowns.
Let the width of the rectangle be denoted by "W" (in ft).
According to the problem, the length of the rectangle is three times the width, so we can express the length as 3W (in ft).
The formula for the perimeter of a rectangle is given by: P = 2L + 2W, where P represents the perimeter, L represents the length, and W represents the width.
From the given information, we know that the perimeter is 48 ft. Substituting the values into the formula, we get:
48 = 2(3W) + 2W
Now, we can solve this equation to find the value of W:
48 = 6W + 2W (distributing the 2)
48 = 8W (combining like terms)
W = 48/8 (dividing both sides by 8)
W = 6
Now that we have the value of W, we can find the length:
L = 3W = 3(6) = 18 ft
The width of the rectangle is 6 ft, and the length is 18 ft.
To calculate the area of a rectangle, we multiply the length by the width:
Area = Length x Width = 18 ft x 6 ft = 108 sq ft
Therefore, the dimensions of the rectangle are 6 ft by 18 ft, and the area is 108 sq ft.