The expression for the perimeter of the pool is 8x + 20 and the cost of fencing the pool is 27.76x + 69.4
How to complete the missing sides?
There are two missing sides in the figure, and they can be calculated using the subtraction operation.
The equations to calculate the missing sides are:
Missing side 1 = 5x - 2 - (-6 + 4x)
Missing side 2 = 12 - x - (3x - 3)
Evaluate the equations
Side 1 = x + 4
Side 2 = 15 - 4x
Hence, the missing sides are x + 4 and 15 - 4x
The perimeter of the pool
This is the sum of the side lengths of the pool.
So, we have:
Perimeter = 5x - 2 + 12 - x - 6 + 4x + 3x - 3 + x + 4 + 15 - 4x
Collect like terms
Perimeter = 5x - x + 4x + x - 4x + 3x - 2 + 12 - 6 - 3 + 4 + 15
Evaluate
Perimeter = 8x + 20
Hence, the perimeter of the pool is 8x + 20
An equation to solve for x
In (b), we have:
P = 8x + 20
Where P represents the perimeter of the pool
The cost of fencing the pool
The cost of fencing the pool is the product of the perimeter and the unit cost per foot.
So, we have:
C = (8x + 20) * 3.47
Expand
C = 27.76x + 69.4
Hence, the cost of fencing the pool is 27.76x + 69.4
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