Question

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?
a) 3 feet
b) 10 feet
c) 4 feet
d) 5 feet

Answer 1

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 we
Then solve the equation for x using the quadratic formula.

ans A 3 feet