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
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![### Triangle Area Problem
#### Problem Statement:
The area of the triangle below is \( \frac{1}{50} \) square inches. What is the length of the base? Express your answer as a fraction in simplest form.
#### Diagram:
- A triangle is depicted.
- The height of the triangle is labeled \( \frac{1}{5} \) inches.
- The right-angle mark at the base of the height signifies that the height is perpendicular to the base.
#### Explanation:
To solve the problem, we use the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Given:
- Area (\( A \)) = \( \frac{1}{50} \) square inches
- Height (\( h \)) = \( \frac{1}{5} \) inches
We need to find the base (\( b \)).
#### Step-by-Step Solution:
1. Write down the formula for the area of a triangle:
\[ A = \frac{1}{2} \times b \times h \]
2. Substitute the given values into the formula:
\[ \frac{1}{50} = \frac{1}{2} \times b \times \frac{1}{5} \]
3. Simplify the equation:
\[ \frac{1}{50} = \frac{1 \times b \times 1}{2 \times 5} \]
\[ \frac{1}{50} = \frac{b}{10} \]
4. Solve for \( b \):
\[ b = \frac{1}{50} \times 10 \]
\[ b = \frac{1 \times 10}{50} \]
\[ b = \frac{10}{50} \]
\[ b = \frac{1}{5} \]
Therefore, the length of the base is
\[ \frac{1}{5} \] inches.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb223a19b-0fd0-443c-881a-6f762159fad5%2F8fe5a945-fbb5-400d-a6cd-564012dd2e3e%2Fcnzd9i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Triangle Area Problem
#### Problem Statement:
The area of the triangle below is \( \frac{1}{50} \) square inches. What is the length of the base? Express your answer as a fraction in simplest form.
#### Diagram:
- A triangle is depicted.
- The height of the triangle is labeled \( \frac{1}{5} \) inches.
- The right-angle mark at the base of the height signifies that the height is perpendicular to the base.
#### Explanation:
To solve the problem, we use the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Given:
- Area (\( A \)) = \( \frac{1}{50} \) square inches
- Height (\( h \)) = \( \frac{1}{5} \) inches
We need to find the base (\( b \)).
#### Step-by-Step Solution:
1. Write down the formula for the area of a triangle:
\[ A = \frac{1}{2} \times b \times h \]
2. Substitute the given values into the formula:
\[ \frac{1}{50} = \frac{1}{2} \times b \times \frac{1}{5} \]
3. Simplify the equation:
\[ \frac{1}{50} = \frac{1 \times b \times 1}{2 \times 5} \]
\[ \frac{1}{50} = \frac{b}{10} \]
4. Solve for \( b \):
\[ b = \frac{1}{50} \times 10 \]
\[ b = \frac{1 \times 10}{50} \]
\[ b = \frac{10}{50} \]
\[ b = \frac{1}{5} \]
Therefore, the length of the base is
\[ \frac{1}{5} \] inches.
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