Question

a family needs to build fencing around their rectangular home and square swimming pool, depicted below.

home: width \\((3 + 10x)\text{ yd}\\), height \\((2 + 5x)\text{ yd}\\)
pool: side length \\((2x)\text{ yd}\\)

the total amount of fencing they need can be written as \\(\quadx + 10\\).

if \\(x = 5\\);
the family needs \\(\quad\\) yards of fencing for their home.

the family needs \\(\quad\\) yards of fencing for their pool.

Explanation:

Calculate the total fencing polynomial

$$
LATEXBLOCK0
$$

Evaluate fencing for the home at x = 5

$$ P_{\text{home}}(5) = 30(5) + 10 = 150 + 10 = 160 $$

Evaluate fencing for the pool at x = 5

$$ P_{\text{pool}}(5) = 8(5) = 40 $$

Answer:

Question 1

The total amount of fencing they need can be written as <blank>38</blank>\(x + 10\).

Question 2

If \(x = 5\);
The family needs <blank>160</blank> yards of fencing for their home.

Question 3

The family needs <blank>40</blank> yards of fencing for their pool.