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:**
In the diagram shown to the right, there are two similar triangles. Find the unknown measurement.
**Diagram Explanation:**
The diagram consists of two right-angled triangles that share a common side, which forms the right angle for both triangles.
1. **Smaller Triangle:**
- It has a height represented as the vertical side, labeled with the number 10.
- The horizontal side, which serves as the base for the triangle, is not labeled separately in this triangle.
2. **Larger Triangle:**
- The height (vertical side) is labeled as 100.
- The base (horizontal side) is the sum of the two smaller horizontal segments, labeled as 10 and 90, making a total of 100 for the complete base.
- The hypotenuse is labeled as \( c \).
**Calculation:**
_Since the triangles are similar, we use the properties of similar triangles (proportional sides):_
\[ \frac{\text{Height of smaller triangle}}{\text{Base of smaller triangle}} = \frac{\text{Height of larger triangle}}{\text{Base of larger triangle}} \]
\[ \frac{10}{10} = \frac{100}{c} \]
_Solve for \( c \):_
\[ 1 = \frac{100}{c} \]
\[ c = 100 \]
**Solution:**
c = 100 (Simplify your answer.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e0f1ad0-c863-431e-a076-23b278670137%2F351722e0-1517-46b9-b6f6-36a49562ce49%2Feylrnyf_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
In the diagram shown to the right, there are two similar triangles. Find the unknown measurement.
**Diagram Explanation:**
The diagram consists of two right-angled triangles that share a common side, which forms the right angle for both triangles.
1. **Smaller Triangle:**
- It has a height represented as the vertical side, labeled with the number 10.
- The horizontal side, which serves as the base for the triangle, is not labeled separately in this triangle.
2. **Larger Triangle:**
- The height (vertical side) is labeled as 100.
- The base (horizontal side) is the sum of the two smaller horizontal segments, labeled as 10 and 90, making a total of 100 for the complete base.
- The hypotenuse is labeled as \( c \).
**Calculation:**
_Since the triangles are similar, we use the properties of similar triangles (proportional sides):_
\[ \frac{\text{Height of smaller triangle}}{\text{Base of smaller triangle}} = \frac{\text{Height of larger triangle}}{\text{Base of larger triangle}} \]
\[ \frac{10}{10} = \frac{100}{c} \]
_Solve for \( c \):_
\[ 1 = \frac{100}{c} \]
\[ c = 100 \]
**Solution:**
c = 100 (Simplify your answer.)
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