A homeowner is enclosing a rectangular garden with a new fence. The garden has a length of… — Armed Services Vocational Aptitude Battery (ASVAB)

A homeowner is enclosing a rectangular garden with a new fence. The garden has a length of $5$ yards and a width of $8$ feet. The homeowner will leave a $36$ -inch wide opening along one of the sides for a wooden gate. If the fencing material costs $\$14.50$ per linear foot, what is the total cost of the fencing material required?

A
$\$333.50$
$\$623.50$ Answer
C
$\$1,740.00$
D
$\$6,235.00$

Answer

\$623.50

To find the correct total cost, all dimensions must first be converted to feet (

5

yards

= 15

feet,

36

inches

= 3

feet). The perimeter is found by adding all four sides (

15 + 15 + 8 + 8 = 46

feet), then subtracting the

3

-foot gate opening to determine that exactly

43

feet of fencing is needed. Multiplying

43

feet by the

\$14.50

cost per foot yields the correct total of

\$623.50

Step-by-Step Solution

Convert all given measurements to a single common unit (feet) since the cost is given per linear foot.

Length:

5 \text{ yards} = 15 \text{ feet}

. Gate width:

36 \text{ inches} = 3 \text{ feet}

Measurements must be in the same units as the pricing rate to calculate accurate costs.

Calculate the total perimeter of the rectangular garden.

P = 2 \times (\text{Length} + \text{Width}) = 2 \times (15 + 8) = 2 \times 23 = 46 \text{ feet}

The perimeter represents the total outline of the garden before accounting for the gate.

Subtract the width of the gate opening from the total perimeter.

46 \text{ feet} - 3 \text{ feet} = 43 \text{ feet}

Fencing material is not needed across the opening where the wooden gate will be installed.

Multiply the required length of fencing by the cost per linear foot.

43 \text{ feet} \times \$14.50/\text{foot} = \$623.50

This provides the final total monetary cost for the required material.

Key Concept

Perimeter and Unit Conversion

Question

Answer

Step-by-Step Solution

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