Answer: The length is 8 ft and the width is 3.5 ft and those are the dimensions.
Step-by-step explanation:
The length of the rectangle is 1 more than double the width so we can represent it by the equation L = 2w + 1 where l is the length and w is the width. We know that to find the area of a rectangle, you will have to multiply the length by the width and the area is 28 ft. so we can represent it by the equation,
w(2w+1) = 28 Now solve for w to find the width
2[tex]w^{2}[/tex] + w = 28 Subtract 28 from both sides for the whole equation to equal zero.
[tex]2w^{2}[/tex] + w -28 = 0 Now solve for w using the quadratic formula
x= -b ± [tex]\sqrt{b^2-4ac} /2a[/tex] In this case, x is representing w(the width)
a = 2 b = 1 c = -28
x = -1 ± [tex]\sqrt{225} / 4[/tex]
x= -1 ± 15 / 4
x= 14/4
x = 3.5
The width is 3.5 ft and the length is 1 more than double the width so
L = 2(3.5) + 1
L = 7 + 1
l = 8
The length is 8
Check
8 * 3.5 = 28
28 = 28
