Class 8 Exam > Class 8 Questions > The perimeter of an isosceles triangle is 32....
Start Learning for Free
The perimeter of an isosceles triangle is 32. The ratio of one of the equal sides to its base is 3:2. Find the area of the triangle.
Most Upvoted Answer
The perimeter of an isosceles triangle is 32. The ratio of one of the ...
Given:
- Perimeter of the isosceles triangle = 32
- Ratio of one of the equal sides to its base = 3:2
To find:
- Area of the triangle
Solution:
Step 1: Determine the sides of the triangle
Let the two equal sides of the triangle be 3x and 3x, and the base be 2x.
The perimeter of the triangle is the sum of all three sides:
3x + 3x + 2x = 32
Simplifying the equation:
8x = 32
x = 4
Therefore, the two equal sides are 3x = 3 * 4 = 12, and the base is 2x = 2 * 4 = 8.
Step 2: Calculate the height of the triangle
In an isosceles triangle, the height can be found using the Pythagorean theorem.
The formula to calculate the height of an isosceles triangle is:
height = √(side^2 - (base/2)^2)
Substituting the values:
height = √(12^2 - (8/2)^2)
height = √(144 - 16)
height = √128
height ≈ 11.31
Step 3: Calculate the area of the triangle
The area of a triangle can be calculated using the formula:
area = (base * height) / 2
Substituting the values:
area = (8 * 11.31) / 2
area = 45.24
Therefore, the area of the isosceles triangle is approximately 45.24 square units.
- Perimeter of the isosceles triangle = 32
- Ratio of one of the equal sides to its base = 3:2
To find:
- Area of the triangle
Solution:
Step 1: Determine the sides of the triangle
Let the two equal sides of the triangle be 3x and 3x, and the base be 2x.
The perimeter of the triangle is the sum of all three sides:
3x + 3x + 2x = 32
Simplifying the equation:
8x = 32
x = 4
Therefore, the two equal sides are 3x = 3 * 4 = 12, and the base is 2x = 2 * 4 = 8.
Step 2: Calculate the height of the triangle
In an isosceles triangle, the height can be found using the Pythagorean theorem.
The formula to calculate the height of an isosceles triangle is:
height = √(side^2 - (base/2)^2)
Substituting the values:
height = √(12^2 - (8/2)^2)
height = √(144 - 16)
height = √128
height ≈ 11.31
Step 3: Calculate the area of the triangle
The area of a triangle can be calculated using the formula:
area = (base * height) / 2
Substituting the values:
area = (8 * 11.31) / 2
area = 45.24
Therefore, the area of the isosceles triangle is approximately 45.24 square units.
Community Answer
The perimeter of an isosceles triangle is 32. The ratio of one of the ...
Attention Class 8 Students!
To make sure you are not studying endlessly, EduRev has designed Class 8 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 8.
|
Explore Courses for Class 8 exam
|
|
Similar Class 8 Doubts
Top Courses for Class 8View all
The perimeter of an isosceles triangle is 32. The ratio of one of the equal sides to its base is 3:2. Find the area of the triangle.
Question Description
The perimeter of an isosceles triangle is 32. The ratio of one of the equal sides to its base is 3:2. Find the area of the triangle. for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The perimeter of an isosceles triangle is 32. The ratio of one of the equal sides to its base is 3:2. Find the area of the triangle. covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perimeter of an isosceles triangle is 32. The ratio of one of the equal sides to its base is 3:2. Find the area of the triangle..
The perimeter of an isosceles triangle is 32. The ratio of one of the equal sides to its base is 3:2. Find the area of the triangle. for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The perimeter of an isosceles triangle is 32. The ratio of one of the equal sides to its base is 3:2. Find the area of the triangle. covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perimeter of an isosceles triangle is 32. The ratio of one of the equal sides to its base is 3:2. Find the area of the triangle..
Solutions for The perimeter of an isosceles triangle is 32. The ratio of one of the equal sides to its base is 3:2. Find the area of the triangle. in English & in Hindi are available as part of our courses for Class 8.
Download more important topics, notes, lectures and mock test series for Class 8 Exam by signing up for free.
Here you can find the meaning of The perimeter of an isosceles triangle is 32. The ratio of one of the equal sides to its base is 3:2. Find the area of the triangle. defined & explained in the simplest way possible. Besides giving the explanation of
The perimeter of an isosceles triangle is 32. The ratio of one of the equal sides to its base is 3:2. Find the area of the triangle., a detailed solution for The perimeter of an isosceles triangle is 32. The ratio of one of the equal sides to its base is 3:2. Find the area of the triangle. has been provided alongside types of The perimeter of an isosceles triangle is 32. The ratio of one of the equal sides to its base is 3:2. Find the area of the triangle. theory, EduRev gives you an
ample number of questions to practice The perimeter of an isosceles triangle is 32. The ratio of one of the equal sides to its base is 3:2. Find the area of the triangle. tests, examples and also practice Class 8 tests.
|
|
Explore Courses for Class 8 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup