A piece of rectangular cloth has an area of 40 square feet. Its length is 3 feet longer than its width. If the width of the rectangular cloth is represented as x, which of the following represents the length?
Its length is 3 feet longer than its width.
so, that would be x+3
34
To find the length of the rectangular cloth, we need to set up an equation based on the given information.
Given:
Area of the cloth = 40 square feet
Length = Width + 3
We can use the formula for the area of a rectangle to set up an equation:
Area = Length × Width
Substituting the given values:
40 = (Width + 3) × Width
Now, let's solve for the length.
Start by distributing the Width to the terms inside the parentheses:
40 = Width² + 3 Width
Rearrange the equation in standard quadratic form:
Width² + 3 Width - 40 = 0
Now, we can factor this quadratic equation:
(Width + 8)(Width - 5) = 0
Setting each factor equal to zero, we have two possible solutions:
Width + 8 = 0 or Width - 5 = 0
Solving the first equation for Width:
Width = -8
Solving the second equation for Width:
Width = 5
Since a negative width doesn't make sense in this context, we discard Width = -8.
Therefore, the width (x) of the rectangular cloth is 5 feet. Now, let's find the length.
Using the relation given in the problem, which states that the length is 3 feet longer than the width, we add 3 to the width:
Length = Width + 3 = 5 + 3 = 8
So, the length of the rectangular cloth is 8 feet.