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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.
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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.
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The perimeter of an isosceles triangle is 32. The ratio of one of the ...
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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.
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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..
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