Answer:
L = [tex]\sqrt{113}[/tex] +4
W = [tex]\sqrt{113}[/tex] -4
or L = 14.63 ft, and W = 6.63 ft
Step-by-step explanation:
Let L be the length and W the width.
We are told that the "length of a rectangle is 8 feet more than its width:"
L = W+8
Area of the rectangle is given by L*W, and is 97 [tex]ft^{2}[/tex]
L*W = 97
Substituting L=W+8, we get:
(W+8)W=97 [tex]ft^{2}[/tex]
[tex]W^{2}[/tex] + 8W = 97
[tex]W^{2}[/tex] + 8W - 97 = 0
The roots to this equation are:
- -4-[tex]\sqrt{113}[/tex], and
- [tex]\sqrt{113}[/tex] -4
Only the second gives a positive value, so W = [tex]\sqrt{113}[/tex] -4
Since L=W+8, the length, L, is [tex]\sqrt{113}[/tex] -4 + 8 or [tex]\sqrt{113}[/tex] +4
In decimal:
L = 14.63 ft, and W = 6.63 ft
