18. An isosceles triangle has an area of 100 in²f the base is 20 in, what is the length of each leg? Round the answer to the nearest tenth. Work: Length of each leg: Work: 19. A kite has diagonals 6.2 and 8 ft. What is the area of the kite? Area: in f₁²
18. An isosceles triangle has an area of 100 in²f the base is 20 in, what is the length of each leg? Round the answer to the nearest tenth. Work: Length of each leg: Work: 19. A kite has diagonals 6.2 and 8 ft. What is the area of the kite? Area: in f₁²
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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Question
![### Geometry Problems
#### Problem 18:
**Question:**
An isosceles triangle has an area of 100 in². If the base is 20 in, what is the length of each leg? Round the answer to the nearest tenth.
**Solution Approach:**
1. **Calculate the height of the triangle** using the formula for the area of a triangle: \( A = \frac{1}{2} \times \text{base} \times \text{height} \).
2. **Use Pythagorean theorem** to find the length of each leg of the isosceles triangle.
**Work Area:**
- The height (h) of the triangle:
\[ 100 = \frac{1}{2} \times 20 \times h \implies h = \frac{100 \times 2}{20} = 10 \, \text{inches} \]
- With the height, use the Pythagorean theorem \((\text{leg})^2 = (\text{height})^2 + \left(\frac{\text{base}}{2}\right)^2\):
\[ (\text{leg})^2 = 10^2 + 10^2 = 100 + 100 \implies \text{leg} = \sqrt{200} = 14.1 \, \text{inches} \]
**Answer:**
\[ \text{Length of each leg: } 14.1 \, \text{in} \]
#### Problem 19:
**Question:**
A kite has diagonals of 6.2 ft and 8 ft. What is the area of the kite?
**Solution Approach:**
1. **Calculate the area of the kite** using the formula for the area of a kite: \( A = \frac{1}{2} \times d1 \times d2 \).
**Work Area:**
- Using the given diagonals:
\[ A = \frac{1}{2} \times 6.2 \times 8 \]
\[ A = \frac{1}{2} \times 49.6 = 24.8 \, \text{ft}^2 \]
**Answer:**
\[ \text{Area: } 24.8 \, \text{ft}^2 \]
These problems involve fundamental](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F397fac9d-f4a8-430e-b095-84d5ec60b33a%2F3ad9d350-e05a-4609-a4ad-b84e095d9b33%2F8kozgce_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Problems
#### Problem 18:
**Question:**
An isosceles triangle has an area of 100 in². If the base is 20 in, what is the length of each leg? Round the answer to the nearest tenth.
**Solution Approach:**
1. **Calculate the height of the triangle** using the formula for the area of a triangle: \( A = \frac{1}{2} \times \text{base} \times \text{height} \).
2. **Use Pythagorean theorem** to find the length of each leg of the isosceles triangle.
**Work Area:**
- The height (h) of the triangle:
\[ 100 = \frac{1}{2} \times 20 \times h \implies h = \frac{100 \times 2}{20} = 10 \, \text{inches} \]
- With the height, use the Pythagorean theorem \((\text{leg})^2 = (\text{height})^2 + \left(\frac{\text{base}}{2}\right)^2\):
\[ (\text{leg})^2 = 10^2 + 10^2 = 100 + 100 \implies \text{leg} = \sqrt{200} = 14.1 \, \text{inches} \]
**Answer:**
\[ \text{Length of each leg: } 14.1 \, \text{in} \]
#### Problem 19:
**Question:**
A kite has diagonals of 6.2 ft and 8 ft. What is the area of the kite?
**Solution Approach:**
1. **Calculate the area of the kite** using the formula for the area of a kite: \( A = \frac{1}{2} \times d1 \times d2 \).
**Work Area:**
- Using the given diagonals:
\[ A = \frac{1}{2} \times 6.2 \times 8 \]
\[ A = \frac{1}{2} \times 49.6 = 24.8 \, \text{ft}^2 \]
**Answer:**
\[ \text{Area: } 24.8 \, \text{ft}^2 \]
These problems involve fundamental
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