Question

a family needs to build fencing around their rectangular home and square swimming pool, depicted below.
pool (2x) yd
home (2 + 5x) yd (3 + 10x) yd
the total amount of fencing they need can be written as
\boxed{}x + 10.
if x = 5;
the family needs
\boxed{} yards of fencing for their home.
the family needs
\boxed{} yards of fencing for their pool.

Explanation:

Step1: Calculate home fencing (perimeter)

Perimeter of rectangle: $2\times(\text{length}+\text{width}) = 2[(3+10x)+(2+5x)]$
Simplify: $2(5+15x) = 10 + 30x$

Step2: Calculate pool fencing (perimeter)

Perimeter of square: $4\times\text{side} = 4(2x) = 8x$

Step3: Total fencing expression

Add home and pool perimeters: $(10+30x)+8x = 38x + 10$

Step4: Substitute $x=5$ for home

$10 + 30(5) = 10 + 150 = 160$

Step5: Substitute $x=5$ for pool

$8(5) = 40$

Answer:

Total fencing coefficient: $38$
Fencing for home: $160$
Fencing for pool: $40$