A garden is in the shape of a rectange. One side of the garden has 20 ft ength the other has a length of x. You pan to build a sidewalk of wdth 4 ft to surrond the garde . The cost to dig and pour concrete is $88 per sq ft. Exoress the cost to buid the sidewallk as a function of x.
outside dimensions = 28 by (x+8)
garden dimensions = 20 by x
concrete area = 28(x+8) - 20 x
= 8 x + 224
cost = 88 (8 x + 224) = 704 x + 19712
To express the cost to build the sidewalk as a function of x, we need to calculate the area of the sidewalk and then multiply it by the cost per square foot.
First, let's find the dimensions of the garden including the sidewalk. The length of one side of the garden is given as 20 ft. Since the sidewalk surrounds the garden on all sides, the length of the garden with the sidewalk will be 20 ft + 2 times the width of the sidewalk (4 ft).
So, the length of the garden with the sidewalk is (20 + 2(4)) ft = (20 + 8) ft = 28 ft.
The other side of the garden has a length of x ft. With the sidewalk, it will be x ft + 2 times the width of the sidewalk (4 ft).
So, the length of the garden with the sidewalk is (x + 2(4)) ft = (x + 8) ft.
To find the area of the garden with the sidewalk, we multiply the length by the width:
Area = (28 ft) * (x + 8 ft)
Now, the cost to build the sidewalk will be the area of the sidewalk multiplied by the cost per square foot, which is $88:
Cost = (88 $/sq ft) * (28 ft) * (x + 8 ft)
Therefore, the cost to build the sidewalk as a function of x is:
Cost(x) = 88 * 28 * (x + 8)