Answer:
3 feet
Step-by-step explanation:
In this question, we are asked to calculate the width of a walkway, given the dimension of the rectangle which the walkway surrounds and the area of the walkway and the rectangle together.
Now, what we need to understand is that the walkway has a uniform width around the rectangle. This means that we add the width around the 4 sides of the rectangle.
Since the width is unknown, let’s represent it with the variable x.
The total length of the garden and walkway will be (12+2x) feet
The total width of the walkway and garden would be (8+2x) feet
Now, if we multiply this two together, what we get is 252 feet
Let’s express this mathematically:
(8+2x)(12+2x) = 252
Let’s open the brackets;
96+ 16x+ 24x + 4x^2 = 252
4x^2 + 40x + 96 = 252
4x^2 + 40x + 96-252 = 0
4x^2 + 40x - 156 = 0
Let’s divide all through by 10. We have;
x^2 + 10x -39 = 0
X^2 +13x-3x-39 = 0
x(x + 13) -3(x+ 13) = 0
(x-3)(x + 13) = 0
x -3 = 0 or x + 13 = 0
x = 3 or -13
We ignore x = -13 since width cannot be negative in size
This Means that the width of the rectangular walkway is 3 feet around
