11 E F N 6. If triangles DEF and NPQ are similar, what is the length of side d? Enter a fraction or a whole number. Provide your answer below: 5/2
11 E F N 6. If triangles DEF and NPQ are similar, what is the length of side d? Enter a fraction or a whole number. Provide your answer below: 5/2
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Educational Content Transcription**
**Title: Similar Triangles and Proportions**
**Problem Statement:**
If triangles \( DEF \) and \( NPQ \) are similar, what is the length of side \( d \)? Enter a fraction or a whole number.
**Diagram Explanation:**
The image contains two similar triangles, \( DEF \) and \( NPQ \):
- Triangle \( DEF \):
- Side \( DE = \frac{5}{2} \)
- Side \( EF = d \)
- Side \( DF = 7 \)
- Triangle \( NPQ \):
- Side \( NP = \frac{11}{2} \)
- Side \( PQ = q \)
- Side \( NQ = 9 \)
**Instructions:**
Provide your answer below for the length of \( d \).
\[ d = \boxed{\phantom{111}} \]
**Mathematical Explanation:**
Since triangles \( DEF \) and \( NPQ \) are similar, their corresponding sides are proportional. Therefore, you can set up the following proportion:
\[
\frac{DE}{NP} = \frac{EF}{PQ} = \frac{DF}{NQ}
\]
Using the given values:
\[
\frac{\frac{5}{2}}{\frac{11}{2}} = \frac{d}{q} = \frac{7}{9}
\]
Solve the proportion for \( d \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50a25d79-a0e0-4f16-9259-569d4f27b8fc%2Ff20fa53c-1843-470f-b4e8-0b481084564b%2Fqkhfu3s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Content Transcription**
**Title: Similar Triangles and Proportions**
**Problem Statement:**
If triangles \( DEF \) and \( NPQ \) are similar, what is the length of side \( d \)? Enter a fraction or a whole number.
**Diagram Explanation:**
The image contains two similar triangles, \( DEF \) and \( NPQ \):
- Triangle \( DEF \):
- Side \( DE = \frac{5}{2} \)
- Side \( EF = d \)
- Side \( DF = 7 \)
- Triangle \( NPQ \):
- Side \( NP = \frac{11}{2} \)
- Side \( PQ = q \)
- Side \( NQ = 9 \)
**Instructions:**
Provide your answer below for the length of \( d \).
\[ d = \boxed{\phantom{111}} \]
**Mathematical Explanation:**
Since triangles \( DEF \) and \( NPQ \) are similar, their corresponding sides are proportional. Therefore, you can set up the following proportion:
\[
\frac{DE}{NP} = \frac{EF}{PQ} = \frac{DF}{NQ}
\]
Using the given values:
\[
\frac{\frac{5}{2}}{\frac{11}{2}} = \frac{d}{q} = \frac{7}{9}
\]
Solve the proportion for \( d \).
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