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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 276 (page 715)

In the following exercises, the triangles are similar. Find the length of the indicated side.
(a) side $d$
(b) side $q$

Short Answer

Expert verified

The required answer is $d = \frac{77}{18}, q = \frac{45}{14}$

Step by step solution

01

Step 1. Given Information

The given figures are

02

Part(a) Step 1. Calculation

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

We will translate into a proportion.

$\frac{d}{\frac{11}{2}} = \frac{7}{9} d = \frac{7}{9} 脳 \frac{11}{2} d = \frac{77}{18}$

03

Part(a) Step 2. Check

We will substitute the value of $x$ in the equation and verify.

$\frac{d}{\frac{11}{2}} = \frac{7}{9} \frac{\frac{77}{18}}{\frac{11}{2}} = \frac{7}{9} \frac{7}{9} = \frac{7}{9}$

Hence, verified.

04

Part (b) Step 1. Calculation

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

We will translate into a proportion.

$\frac{\frac{5}{2}}{q} = \frac{7}{9} \frac{5}{2} 脳 \frac{9}{7} = q q = \frac{45}{14}$

05

Part (b) Step 2. Check

We will substitute the value of $x$ in the equation and verify.

$\frac{\frac{5}{2}}{q} = \frac{7}{9} \frac{\frac{5}{2}}{\frac{45}{14}} = \frac{7}{9} \frac{7}{9} = \frac{7}{9}$

Hence, verified.

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