Chris lambton just designed a cloister a rectangle garden surrounded by a covered walkway on all four side the outside dimensions of garden 12 feet by 8 feet and the area of the garden the walkway together is 252 square feet what is the width of the walkway

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