SOLUTION: A rectangular garden is 12 feet by 5 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 138 square feet?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A rectangular garden is 12 feet by 5 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 138 square feet?       Log On


   

Question 190807: A rectangular garden is 12 feet by 5 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 138 square feet?
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the width of the path.
Then the dimensions of the rectangle formed by the outer edges of the path can is:
Length: 2x + 12
Width: 2x + 5
So its area = (2x+12)(2x + 5) = 2(x +6)(2x+5)
The area of the garden is 12x5
Therefore the area of the gravel path = 2(x+6)(2x+5)-12x5
Setting the area of the gravel path equal to 138, we have
2(x+6)(2x+5)-12x5 = 138
Dividing both sides by 2 to simplify it, we have
(x+6)(2x+5)-6x5 = 69
Solving the equation for x, we have
2x%5E2+%2B17x%2B30-30=69
2x%5E2+%2B17x-69=0
Then solve the equation for x using the quadratic formula.