Question

solving scale problems using proportions
finding the missing dimension in an original figure
consider the enlargement of the rectangle.
use the proportion to find the missing dimension of the
original rectangle.

1. set up the proportion:

\\( \frac { 3 } { 5 } = \frac { x } { 20 } \\)

1. use cross products:

\\( 12 ( x ) = 20 ( \frac { 3 } { 5 } ) \\)

1. simplify:

\\( 12 x = \square \\)

1. divide:

\\( x = \square \\)

Explanation:

Step1: Set up the proportion

Since the rectangles are similar, the ratios of their corresponding sides are equal. So, \(\frac{3}{5}=\frac{x}{20}\)

Step2: Use cross - products

Cross - multiplying gives \(12\times x = 20\times\frac{3}{5}\)

Step3: Simplify

First, calculate \(20\times\frac{3}{5}\). \(20\div5 = 4\), and \(4\times3=12\). So, \(12x = 12\)

Step4: Divide

Divide both sides of the equation \(12x = 12\) by \(12\). \(\frac{12x}{12}=\frac{12}{12}\), which gives \(x = 1\)

Answer:

\(x = 1\)