Chapter 6.6, Problem 43E

To determine

To calculate: The ratio of object’s length to object’s width in the scale drawing.

Answer to Problem 43E

The ratio of object’s length to object’s width in the scale drawing is $3:2$ .

Explanation of Solution

Given information:

The ratio of length of an object to its width is $3:2$ .

Calculation:

To find ratio of object’s length to object’s width in the scale drawing use properties of similar figures. Since a scale drawing is a drawing that is similar to the object it represents, the ratio of corresponding sides of the scale drawing and the object will be equal.

Assume the length and breadth of the object to be $3x$ and $2x$ respectively.

Let length and breadth of the scale drawing be $L$ and $B$ respectively.

  $\begin{array}{l}\frac{\text{Length of scale drawing}}{\text{Length of object}}=\frac{\text{Width of scale drawing}}{\text{Width of object}}\text{ [Write proportion]}\\ \frac{L}{3x}=\frac{B}{2x}\text{ [Substitute values]}\\ \frac{L}{B}=\frac{3x}{2x}\text{ [Form ratio of }L\text{ and }B\text{]}\\ \frac{L}{B}=\frac{3}{2}\text{ [Divide out common units]}\end{array}$

Therefore, the ratio of object’s length to object’s width in the scale drawing is $3:2$ .