Answer:
"The family needs 160 yards of fencing for their home."
"The family needs 40 yards of fencing for their pool."
Step-by-step explanation:
Home:
The home is rectangular in shape and the perimeter is given by:
P = 2 (l + w)
Where
P is perimeter
l is length
w is width
Let's find perimeter of home given l = 2+5x and w=3+10x
P = 2 (2+5x+3+10x)
P = 2 (5+15x)
P = 10 + 30x
Since, x = 5, it will be 10 + 30(5) = 160 yards of fencing needed
Pool:
The pool is square and the perimeter would be given as:
P = 4s
Where
P is perimeter
s is side length
The side length is given as 2x, so perimeter is:
P = 4(2x) = 8x
Given x = 5,
P = 8(5) = 40 yards of fencing needed
The side length of the square pool and the length and with of the home
are given as function of the variable x.
Response:
If x = 5;
The given parameters are;
Side length of the square pool = 2·x
Dimensions of the rectangular home are;
Width = (2 + 5·x)
Length = (3 + 10·x)
The total amount of fencing needed is given by the sum of the
perimeter of the square pool and the perimeter of the home as follows;
Perimeter of the pool = 4 × 2·x = 8·x
Perimeter of the home = 2 × (((2 + 5·x) + (3 + 10·x)) = 30·x + 10
The total fencing = 8·x + 30·x + 10 = 38·x + 10
If x = 5, we have;
Fencing for their home = 30 × 5 + 10 = 160
Fencing for the pool = 8 × 5 = 40
Therefore;
If x = 5;
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