Chapter 7, Problem 23CP

To determine

To Find: The unknown side of a rectangle, which is similar to another rectangle with both known sides.

Answer to Problem 23CP

The length of $\overline{EF}$ is $9.6$

Explanation of Solution

Given: Length of both the sides of one triangle and length of only one side in a triangle similarto the first one.

  

Concept Used:

• If two triangles are similar, then the ratios of their corresponding sides are in proportion.
• In a proportion, the cross products must be equal.

The ratios of the corresponding sides are $\frac{8}{5}$ and $\frac{\overline{EF}}{6}$ .

Since the ratios are in proportion, their cross products $8\times 6$ and $\overline{EF}\times 5$ are equal.

  $\Rightarrow 8\times 6=\overline{EF}\times 5$

Divide the equation by $5$ to get

  $\overline{EF}=\frac{8\times 6}{5}=\frac{48}{5}=9.6$