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 Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter9: Roots And Radicals
Section9.4: Multiply Square Roots
Problem 311E: An artist wants to make a small monument in the shape of a square base topped by a right triangle,...
Related questions
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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,