A square parking lot has an area of 169 yards. There is a sidewalk along one side of the parking lot. How long is the sidewalk? Use an equation to solve this. Show all of your work. *
Answers
Step-by-step explanation:
Let's begin by using letters to represent our two unknowns:
L = length of rectangle
W = width of rectangle
Now let's see how we can express one unknown in terms of the other, so that have one unknown to solve for in our rectangle area equation (A = L x W):
L = W + 8 (length is 8 yards more than width)
Let's plug our expression for L in terms of W into our rectangle area equation (A = L x W) and solve for W:
(W + 8) x W = 180 (given area)
(W)(W) + (8)(W) = 180
W2 + 8W = 180
W2 + 8W - 180 = 0
Find 2 factors of -180 which also add up to 8
(factors are +18 and -10)
Set each factor to zero and solve for W:
W + 18 = 0 | W - 10 = 0
W = -18 | W = 10
We reject negative answer as we cannot have a negative measurement:
W = 10 yds. (width of rectangle)
Now using our W expression for L, we can solve for L:
L = W + 8
L = 10 + 8
L = 18 yds. (length of rectangle)
Finally, we can verify that our answers are correct by seeing if the product of our answers (Length x Width) is equal to the given Area of the rectangle:
A = L x W
180 = 18 x 10
180 = 180 (answers verified)
HOPE IT HELPS YOU MATE