Question 190807
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^2 +17x+30-30=69}}}
{{{2x^2 +17x-69=0}}}
Then solve the equation for x using the quadratic formula.