Question

use the proportion of the triangle enlargement to find the missing measure of the enlarged triangle.

1. set up the proportion.

\\( \frac { 6 } { 16 } = \frac { 9 } { x } \\)

1. use cross product.

\\( 9 ( 16 ) = 6 x \\)

1. simplify.

\\( 144 = \\)

1. divide.

\\( = x \\)

Explanation:

Step1: Cross - product

For the proportion \(\frac{6}{16}=\frac{9}{x}\), by cross - product rule \(a/b = c/d\) implies \(ad=bc\). So \(6x = 9\times16\).

Step2: Simplify the right - hand side

Calculate \(9\times16\). \(9\times16=(10 - 1)\times16=10\times16-1\times16 = 160 - 16=144\). So the equation becomes \(6x = 144\).

Step3: Solve for \(x\)

Divide both sides of the equation \(6x = 144\) by \(6\). \(\frac{6x}{6}=\frac{144}{6}\).

Answer:

\(x = 24\)