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
Related questions
Question
![**Problem Statement:**
Find the value for \( x \).
**Given:**
ABCD ∼ JKLH
**Diagram Details:**
The figure shows two rectangles, ABCD and JKLH, indicating that they are similar.
1. Rectangle ABCD:
- Side \( AB = 4 \)
- Side \( AD = 5 \)
2. Rectangle JKLH:
- Side \( HJ = 4x + 2 \)
- Side \( HL = 3x + 2 \)
**Solution Step:**
To find the value of \( x \), use the property of similar rectangles where the ratio of corresponding sides is equal:
\[
\frac{AB}{HJ} = \frac{AD}{HL}
\]
Plug in the given values to solve for \( x \).
**Input for Verification:**
An input box labeled \( x = \) is provided for entering the value of \( x \).
**Action Button:**
A "Submit Question" button is available to submit the solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c22293a-3ae6-4ac2-9c37-c12acd82a0e8%2F2357234a-15e0-4dd6-beac-89751ad693f7%2F66o9f8x_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the value for \( x \).
**Given:**
ABCD ∼ JKLH
**Diagram Details:**
The figure shows two rectangles, ABCD and JKLH, indicating that they are similar.
1. Rectangle ABCD:
- Side \( AB = 4 \)
- Side \( AD = 5 \)
2. Rectangle JKLH:
- Side \( HJ = 4x + 2 \)
- Side \( HL = 3x + 2 \)
**Solution Step:**
To find the value of \( x \), use the property of similar rectangles where the ratio of corresponding sides is equal:
\[
\frac{AB}{HJ} = \frac{AD}{HL}
\]
Plug in the given values to solve for \( x \).
**Input for Verification:**
An input box labeled \( x = \) is provided for entering the value of \( x \).
**Action Button:**
A "Submit Question" button is available to submit the solution.
Expert Solution
Step 1
Given that the rectangle .
Find the value of .
A rectangle is shape having four sides , four corners and four right angles. The opposite sides of a rectangle are equal and parallel.
If two rectangles are said to be similar, their corresponding sides have to be proportional.
Step by step
Solved in 2 steps
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