Chapter 7: Q.753. (page 740)

$∆ A B C$ is similar to $∆ X Y Z$ . The lengths of two sides of each triangle are given in the figure. Find the length of the third sides.

Short Answer

Expert verified

The value for the side $b$ is $9$ and the value for the side $x$ is $2 \frac{1}{3}$ .

Step by step solution

Step 1. Given information.

The given figure is:

Step 2. To find the value of b.

Since the given triangles are similar, the corresponding angle measures are equal and their corresponding sides have the same ratio.

$\begin{array}{rcl} \frac{8}{2 \frac{2}{3}} & = & \frac{b}{3} \\ \frac{8}{\frac{8}{3}} & = & \frac{b}{3} \\ \frac{8 \times 3}{8} & = & \frac{b}{3} \\ 3 & = & \frac{b}{3} \\ b & = & 3 \times 3 \\ b & = & 9 \end{array}$

Step 3. To find the value of x.

Since the given triangles are similar, the corresponding angle measures are equal and their corresponding sides have the same ratio.

\begin{array}{rcl} \frac{8}{2 \frac{2}{3}} & = & \frac{7}{x} \\ \frac{8}{\frac{8}{3}} & = & \frac{7}{x} \\ \frac{8 \times 3}{8} & = & \frac{7}{x} \\ 3 & = & \frac{7}{x} \\ x & = & \frac{7}{3} \\ x & = & 2 \frac{1}{3} \end{array}

Step 4. Simplified answer.

Hence, the required solution is $b = 9$ and $x = 2 \frac{1}{3}$ .

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$∆ A B C$ is similar to $∆ X Y Z$ . The lengths of two sides of each triangle are given in the figure. Find the length of the third sides.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. To find the value of b.

Step 3. To find the value of x.

Step 4. Simplified answer.

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∆ABCis similar to ∆XYZ. The lengths of two sides of each triangle are given in the figure. Find the length of the third sides.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. To find the value of b.

Step 3. To find the value of x.

Step 4. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Probability and Statistics

Applied Mathematics

Logic and Functions

Geometry

Study anywhere. Anytime. Across all devices.

$∆ A B C$ is similar to $∆ X Y Z$ . The lengths of two sides of each triangle are given in the figure. Find the length of the third sides.