Question

fencing the figure shows dereks house and his backyard on a coordinate grid. derek is planning to fence in the play area in his backyard. part of the play area is enclosed by the house and does not need to be fenced. each unit on the coordinate grid represents 5 feet. the cost for the fencing materials and installation is $10 per foot.
how much will it cost derek to install the fence?

Explanation:

Step1: Count the number of units for the fence

Count the number of units along the sides of the play - area that need fencing. Assume the play - area has side lengths (by counting units) of \(a\) and \(b\). Let's say after counting, the sum of the lengths of the sides that need fencing (in units) is \(n\). For example, if we count 8 units for the vertical sides and 4 units for the horizontal sides (excluding the side enclosed by the house), \(n=(8 + 4)\) units.

Step2: Convert units to feet

Since each unit represents 5 feet, the length \(L\) of the fence in feet is \(L = 5n\). Using \(n=(8 + 4)=12\) units, \(L=5\times12 = 60\) feet.

Step3: Calculate the cost

The cost \(C\) of the fence is given by the formula \(C=\text{Cost per foot}\times\text{Length of fence}\). Given the cost per foot is \(\$30\), \(C = 30\times L\). Substituting \(L = 60\) feet, \(C=30\times60=\$1800\).

Answer:

\(1800\)