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The hypotenuse of an isosceles right triangle is 10 cm . find its area using heron's formula?
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The hypotenuse of an isosceles right triangle is 10 cm . find its area...
Understanding the Isosceles Right Triangle
An isosceles right triangle has two equal sides and a right angle. The relationship between the sides and the hypotenuse can be defined as:
- If the legs are of length 'a', then by the Pythagorean theorem, a² + a² = (hypotenuse)².
- Thus, 2a² = 10², leading to a² = 50, so a = √50 or approximately 7.07 cm.
Calculating the Area Using Heron's Formula
1. Determine the Side Lengths:
- The triangle has two equal sides (a) and a hypotenuse (c):
- a ≈ 7.07 cm
- c = 10 cm
2. Calculate the Semi-Perimeter (s):
- The semi-perimeter s is given by:
- s = (a + a + c) / 2
- s = (7.07 + 7.07 + 10) / 2
- s ≈ 12.07 cm
3. Apply Heron's Formula:
- Heron's formula states that the area (A) is:
- A = √[s(s-a)(s-a)(s-c)]
- Plugging in values:
- A = √[12.07(12.07-7.07)(12.07-7.07)(12.07-10)]
- A = √[12.07 * 5 * 5 * 2.07]
4. Final Area Calculation:
- Calculate each part:
- A = √[12.07 * 25 * 2.07]
- A ≈ √(625.22)
- A ≈ 25 cm²
Conclusion
The area of the isosceles right triangle with a hypotenuse of 10 cm is approximately 25 cm².
An isosceles right triangle has two equal sides and a right angle. The relationship between the sides and the hypotenuse can be defined as:
- If the legs are of length 'a', then by the Pythagorean theorem, a² + a² = (hypotenuse)².
- Thus, 2a² = 10², leading to a² = 50, so a = √50 or approximately 7.07 cm.
Calculating the Area Using Heron's Formula
1. Determine the Side Lengths:
- The triangle has two equal sides (a) and a hypotenuse (c):
- a ≈ 7.07 cm
- c = 10 cm
2. Calculate the Semi-Perimeter (s):
- The semi-perimeter s is given by:
- s = (a + a + c) / 2
- s = (7.07 + 7.07 + 10) / 2
- s ≈ 12.07 cm
3. Apply Heron's Formula:
- Heron's formula states that the area (A) is:
- A = √[s(s-a)(s-a)(s-c)]
- Plugging in values:
- A = √[12.07(12.07-7.07)(12.07-7.07)(12.07-10)]
- A = √[12.07 * 5 * 5 * 2.07]
4. Final Area Calculation:
- Calculate each part:
- A = √[12.07 * 25 * 2.07]
- A ≈ √(625.22)
- A ≈ 25 cm²
Conclusion
The area of the isosceles right triangle with a hypotenuse of 10 cm is approximately 25 cm².
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The hypotenuse of an isosceles right triangle is 10 cm . find its area using heron's formula?
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The hypotenuse of an isosceles right triangle is 10 cm . find its area using heron's formula? 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 The hypotenuse of an isosceles right triangle is 10 cm . find its area using heron's formula? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The hypotenuse of an isosceles right triangle is 10 cm . find its area using heron's formula?.
The hypotenuse of an isosceles right triangle is 10 cm . find its area using heron's formula? 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 The hypotenuse of an isosceles right triangle is 10 cm . find its area using heron's formula? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The hypotenuse of an isosceles right triangle is 10 cm . find its area using heron's formula?.
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