Chapter 5.8, Problem 9IP

To determine

To prepare: A scale drawing of the skatepark based on the given scale.

Answer to Problem 9IP

Thescale drawing of the skatepark is given below.

Explanation of Solution

Given information:

The length of the skatepark is 48 yards and the width is 24 yards.The scale is $\frac{1}{4}\text{in}\text{.}=8\text{yd}$ . Let assume the grid paper is $\frac{1}{4}\text{in}\text{.}$ .

Calculation:

Simplify the scale.

  $\begin{array}{c}\frac{1}{4}\text{in}\text{.}=8\text{yd}\\ 1\text{in}\text{.}=32\text{yd}\end{array}$

To draw the scale drawing of the skatepark, find the length and the width on the drawing divide these by $\frac{1}{4}$ .

Let the length of the scale drawing is $x$ and the width of the scale drawing is $y$ .

Calculate the length of the scale drawing.

  $\begin{array}{c}\frac{1\text{in}\text{.}}{32\text{yd}}=\frac{x\text{in}\text{.}}{48\text{yd}}\\ x=\frac{1\times 48}{32}\\ =1.5\text{in}.\end{array}$

Since the size of the square in the grid paper is $\frac{1}{4}\text{in}\text{.}$ . Find the number of squares along the length.

  $\frac{1.5\text{in}.}{\frac{1}{4}\text{in}\text{.}}=6\text{squares}$

Calculate the width of the scale drawing.

  $\begin{array}{c}\frac{1\text{in}\text{.}}{32\text{yd}}=\frac{y\text{in}\text{.}}{24\text{yd}}\\ y=\frac{1\times 24}{32}\\ =0.75\text{in}.\end{array}$

Since the size of the square in the grid paper is $\frac{1}{4}\text{in}\text{.}$ . Find the number of squares along the width.

  $\frac{0.75\text{in}.}{\frac{1}{4}\text{in}\text{.}}=3\text{squares}$

Draw the scale drawing of the skatepark on the grid paper.