A rectangle has a length 2 ft less than three times its width. What is the area of the rectangle when its width is 2 ft?
(1 point)
Responses
8 square ft
6 square ft
12 square ft
10 square ft
Let's solve this step by step.
Let's say the width of the rectangle is x ft.
According to the problem, the length is 2 ft less than three times the width, which can be represented as 3x - 2 ft.
The formula for the area of a rectangle is length * width.
So, in this case, the area would be (3x - 2) * x.
We are given that the width is 2 ft, which means x = 2.
Plugging this value into the equation, we get:
Area = (3 * 2 - 2) * 2
= (6 - 2) * 2
= 4 * 2
= 8 square ft.
Therefore, the correct answer is 8 square ft.
To find the area of the rectangle, we first need to determine the dimensions of the rectangle.
Let's represent the width of the rectangle as "w" ft.
According to the problem, the length of the rectangle is 2 ft less than three times its width. So, the length would be (3w - 2) ft.
Now, we can substitute the given width (w = 2 ft) into the equation:
Length = 3w - 2 = 3(2) - 2 = 6 - 2 = 4 ft
The area of the rectangle is given by the product of the length and the width:
Area = Length x Width = 4 ft x 2 ft = 8 square ft
Therefore, the correct answer is 8 square ft.