Homework Help is Here – Start Your Trial Now!
Math
Geometry
**Similar Figures / Proportion (Level 3)** **Triangle JKL is similar to triangle MNO. Find the measure of side OM. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale.** ![Triangle JKL and Triangle MNO](image.png) **Figures Explanation:** - **Triangle JKL:** - Side JL measures **40** units. - Side LK measures **19** units. - Vertex J is on the left, vertex K is at the bottom right, and vertex L is at the top. - **Triangle MNO:** - Side NO measures **58** units. - Side OM is labeled as **x** (unknown value to be calculated). - Vertex N is at the bottom left, vertex O is at the bottom right, and vertex M is at the top. **Solution:** 1. To find the measure of side **OM** (denoted as **x**), we use the property of similar triangles where corresponding sides are proportional. 2. Set up the proportion using corresponding sides of the two triangles: \[ \frac{JL}{MN} = \frac{LK}{OM} \] \[ \frac{40}{58} = \frac{19}{x} \] 3. Cross multiply to solve for \( x \): \[ 40x = 58 \times 19 \] \[ 40x = 1102 \] \[ x = \frac{1102}{40} \] \[ x = 27.55 \] (rounded to the nearest tenth) Answer box for user input: \[ \boxed{27.6} \]

**Similar Figures / Proportion (Level 3)** **Triangle JKL is similar to triangle MNO. Find the measure of side OM. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale.** ![Triangle JKL and Triangle MNO](image.png) **Figures Explanation:** - **Triangle JKL:** - Side JL measures **40** units. - Side LK measures **19** units. - Vertex J is on the left, vertex K is at the bottom right, and vertex L is at the top. - **Triangle MNO:** - Side NO measures **58** units. - Side OM is labeled as **x** (unknown value to be calculated). - Vertex N is at the bottom left, vertex O is at the bottom right, and vertex M is at the top. **Solution:** 1. To find the measure of side **OM** (denoted as **x**), we use the property of similar triangles where corresponding sides are proportional. 2. Set up the proportion using corresponding sides of the two triangles: \[ \frac{JL}{MN} = \frac{LK}{OM} \] \[ \frac{40}{58} = \frac{19}{x} \] 3. Cross multiply to solve for \( x \): \[ 40x = 58 \times 19 \] \[ 40x = 1102 \] \[ x = \frac{1102}{40} \] \[ x = 27.55 \] (rounded to the nearest tenth) Answer box for user input: \[ \boxed{27.6} \]

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
See similar textbooks
icon
Related questions
Question
**Similar Figures / Proportion (Level 3)** **Triangle JKL is similar to triangle MNO. Find the measure of side OM. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale.** ![Triangle JKL and Triangle MNO](image.png) **Figures Explanation:** - **Triangle JKL:** - Side JL measures **40** units. - Side LK measures **19** units. - Vertex J is on the left, vertex K is at the bottom right, and vertex L is at the top. - **Triangle MNO:** - Side NO measures **58** units. - Side OM is labeled as **x** (unknown value to be calculated). - Vertex N is at the bottom left, vertex O is at the bottom right, and vertex M is at the top. **Solution:** 1. To find the measure of side **OM** (denoted as **x**), we use the property of similar triangles where corresponding sides are proportional. 2. Set up the proportion using corresponding sides of the two triangles: \[ \frac{JL}{MN} = \frac{LK}{OM} \] \[ \frac{40}{58} = \frac{19}{x} \] 3. Cross multiply to solve for \( x \): \[ 40x = 58 \times 19 \] \[ 40x = 1102 \] \[ x = \frac{1102}{40} \] \[ x = 27.55 \] (rounded to the nearest tenth) Answer box for user input: \[ \boxed{27.6} \]
Transcribed Image Text:**Similar Figures / Proportion (Level 3)** **Triangle JKL is similar to triangle MNO. Find the measure of side OM. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale.** ![Triangle JKL and Triangle MNO](image.png) **Figures Explanation:** - **Triangle JKL:** - Side JL measures **40** units. - Side LK measures **19** units. - Vertex J is on the left, vertex K is at the bottom right, and vertex L is at the top. - **Triangle MNO:** - Side NO measures **58** units. - Side OM is labeled as **x** (unknown value to be calculated). - Vertex N is at the bottom left, vertex O is at the bottom right, and vertex M is at the top. **Solution:** 1. To find the measure of side **OM** (denoted as **x**), we use the property of similar triangles where corresponding sides are proportional. 2. Set up the proportion using corresponding sides of the two triangles: \[ \frac{JL}{MN} = \frac{LK}{OM} \] \[ \frac{40}{58} = \frac{19}{x} \] 3. Cross multiply to solve for \( x \): \[ 40x = 58 \times 19 \] \[ 40x = 1102 \] \[ x = \frac{1102}{40} \] \[ x = 27.55 \] (rounded to the nearest tenth) Answer box for user input: \[ \boxed{27.6} \]
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS