Answer:
The expression representing the width is 3+2L
The width is 9ft
Explanation:
Area of a rectangle = Length×width
A = L × W...(1)
Let the length be represented as L
Since the width of the rectangle is 3feet longer than two times its length, this is expressed as:
First, width is twice as long as the length i.e W = 2L
If the resulting width is now 3 feet longer, the final width of the rectangle will be expressed as:
W = 3+2L...(2)
Area (A) = 27ft
Substituting equation 2 into 1, we have;
A = L(3+2L)
A = 3L+2L²
27 = 3L+2L²
2L²+3L-27 = 0
Factorizing the resulting equation
(2L²+9L)-(6L-27) = 0
L(2L+9)-3(2L+9) = 0
L-3 = 0 and 2L+9 = 0
L = 3 and L = -9/2
Disregarding the negative value and substituting L = 3 into equation 2 to get the width
W = 3+2(3)
W = 3+6
W = 9ft