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If the area of an isosceles triangle is 12cm2 and it's base 8 cm then find it's perimeter?
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If the area of an isosceles triangle is 12cm2 and it's base 8 cm then ...
Area and Base of the Triangle
To find the perimeter of the isosceles triangle, we start with the given values:
- Area = 12 cm²
- Base = 8 cm
Finding the Height
We can use the formula for the area of a triangle:
Area = (1/2) × base × height
From this, we can derive the height:
- 12 = (1/2) × 8 × height
- 12 = 4 × height
- height = 3 cm
Finding the Length of the Equal Sides
In an isosceles triangle, the height divides the triangle into two congruent right triangles. Each side of the triangle can be calculated using the Pythagorean theorem.
- Half of the base = 4 cm
- Height = 3 cm
Using the Pythagorean theorem:
- Let the length of each equal side be "s".
- s² = 4² + 3²
- s² = 16 + 9
- s² = 25
- s = 5 cm
Calculating the Perimeter
The perimeter of an isosceles triangle is given by:
Perimeter = base + 2 × length of equal sides
Substituting the values we found:
- Perimeter = 8 + 2 × 5
- Perimeter = 8 + 10
- Perimeter = 18 cm
Final Answer
Thus, the perimeter of the isosceles triangle is 18 cm.
To find the perimeter of the isosceles triangle, we start with the given values:
- Area = 12 cm²
- Base = 8 cm
Finding the Height
We can use the formula for the area of a triangle:
Area = (1/2) × base × height
From this, we can derive the height:
- 12 = (1/2) × 8 × height
- 12 = 4 × height
- height = 3 cm
Finding the Length of the Equal Sides
In an isosceles triangle, the height divides the triangle into two congruent right triangles. Each side of the triangle can be calculated using the Pythagorean theorem.
- Half of the base = 4 cm
- Height = 3 cm
Using the Pythagorean theorem:
- Let the length of each equal side be "s".
- s² = 4² + 3²
- s² = 16 + 9
- s² = 25
- s = 5 cm
Calculating the Perimeter
The perimeter of an isosceles triangle is given by:
Perimeter = base + 2 × length of equal sides
Substituting the values we found:
- Perimeter = 8 + 2 × 5
- Perimeter = 8 + 10
- Perimeter = 18 cm
Final Answer
Thus, the perimeter of the isosceles triangle is 18 cm.
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If the area of an isosceles triangle is 12cm2 and it's base 8 cm then find it's perimeter?
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If the area of an isosceles triangle is 12cm2 and it's base 8 cm then find it's perimeter? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If the area of an isosceles triangle is 12cm2 and it's base 8 cm then find it's perimeter? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the area of an isosceles triangle is 12cm2 and it's base 8 cm then find it's perimeter?.
If the area of an isosceles triangle is 12cm2 and it's base 8 cm then find it's perimeter? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If the area of an isosceles triangle is 12cm2 and it's base 8 cm then find it's perimeter? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the area of an isosceles triangle is 12cm2 and it's base 8 cm then find it's perimeter?.
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