Answer: the length of the walkway is 30.64ft
The width of the walkway is 8.16ft
Step-by-step explanation:
Since the walkway has length and width, it is rectangular in shape. For a rectangle, the two lengths and two widths are equal. The area is expressed as length, L × Width,W.
The front walkway from the street to Pam's house has an area of 250ft^2. It means that
LW = 250
Its length is two less than four times its width. It means
L = 4W - 2
Substituting L = 4W - 2 into LW = 250, it becomes
W(4W - 2) = 250
4W^2 - 2W- 250 = 0
Using the general formula for quadratic equations,
W = [- b ± √b^2 - 4ac]/2a
a = 4
b = -2
c = - 250
W= [- - 2 ±√-2^2 -4(4 × -250)]/2×4
= (2 ± √4 + 4000)/8
= (2 ±63.277)/8
W= (2 + 63.277)/8 or W = (2 - 63.277)/8
W = 8.16 or W = - 7.91
Since the width cannot be negative, width = 8.16 ft
LW = 250
8.16L = 250
L = 250/8.16 = 30.64 ft
