Question 550976: Knox College is creating a new rectangular parking lot. The length is 0.07 mile longer than the width and the area of the parking lot is 0.026 square mile. Find the length and width of the parking lot.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the width of the parking lot is .13 miles.
the length of the parking lot is .2 miles.
.2 * .13 = .026 equals the area of the parking lot in square miles.
problem is solved as follows:
L = length of the parking lot.
W = width of the parking lot.
area of the parking lot is equal to L * W = .026
since the length of the parking lot is equal to .07 miles more than the width, this equation becomes:
(W + .07) * W = .026
simplify this equation to get:
W^2 + .07 * W = .026
subtract .026 from both sides of this equation to get:
W^2 + .07W - .026 = 0
this is a quadratic equation that can be solved using the quadratic formula of:
W = (-b +/- sqrt(b^2-4ac))/(2a) where:
a = 1
b = .07
c = -.026
use that formula to get:
W = (-.07 +/- .33)/2
W = -.2 or W = .13
W = -.2 is rejected because the width of the parking lot can't be negative.
only possible answer is W = .13
if W is .13, then L = .13 + .07 = .2
.2*.13 = .026 which is the area of the parking lot.
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