Answer: The equation is
W^2 + 30W - 175 = 0
And the width of the walkway = 5 meters
Step-by-step explanation: For the square garden we have the dimensions as 17 meters by 13 meters. Also there is a walkway that borders all four sides of the rectangular garden. So the dimensions of the garden plus walkway, can be derived as;
L= 17 + W and
W = 13 + W
If the area of the entire shape (garden plus walkway inclusive) is given as 396 square meters, then we can write the equation as follows
Area of a rectangle = L x W
Area of a rectangle= (17 + W) x (13 + W)
396 = 221 + 17W + 13W + W^2
396 - 221 = 30W + W^2
(Remember that when a positive value crosses to the other side of an equation it becomes negative and vice versa)
175 = 30W + W^2
W^2 + 30W - 175 = 0
Having found the equation (a quadratic equation) that can be used to determine the width of the walkway, which is W, we can now proceed to calculate W as follows
W^2 + 30W - 175 = 0
By factorizing we now arrive at
W^2 +35W - 5W - 175 = 0
(W + 35) (W - 5) = 0
That means,
Either W + 35 = 0, hence W = -35
OR
W - 5 = 0, hence W = 5
Since W cannot be a negative value, we know that W= 5
Therefore the width of the walkway is 5 meters
