Answer:
The length of the rectangle is 12 inches.
Step-by-step explanation:
Let the length and width of the rectangle be represented as l and w respectively.
Thus,
l = 2w+ 4
area = 48 square inches
So that,
Area of a rectangle = l x w
48 = (2w + 4) x w
= 2[tex]w^{2}[/tex] + 4w
2[tex]w^{2}[/tex] + 4w - 48 = 0
Divide through by 2 to have;
[tex]w^{2}[/tex] + 2w - 24 = 0
([tex]w^{2}[/tex] - 4w) (6w - 24)
w(w - 4) + 6(w - 4)
Thus,
(w - 4) or (w + 6)
w - 4 = 0 or w + 6 = 0
w = 4 or w = -6\
Therefore, the width of the rectangle is 4 inches. Then,
length, l = 2w + 4
= 2 (4) + 4
= 12 inches
The length of the rectangle is 12 inches.
