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If the base of a right angle - triangle is 15 cm and it's hypotenuse is 25 find it's area?
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If the base of a right angle - triangle is 15 cm and it's hypotenuse i...
Understanding the Problem
To find the area of a right triangle, we need to know the base and height. In this case, the base is given as 15 cm and the hypotenuse as 25 cm. We need to calculate the height using the Pythagorean theorem.
Pythagorean Theorem
The Pythagorean theorem states that in a right triangle:
where c is the hypotenuse, and a and b are the other two sides (base and height). Here, we know:
Calculating the Height
Using the Pythagorean theorem:
Finding the Area
The area (A) of a right triangle can be calculated using the formula:
Conclusion
The area of the triangle is 150 cm². This process demonstrates the relationship between the sides of a right triangle and how to compute its area effectively.
To find the area of a right triangle, we need to know the base and height. In this case, the base is given as 15 cm and the hypotenuse as 25 cm. We need to calculate the height using the Pythagorean theorem.
Pythagorean Theorem
The Pythagorean theorem states that in a right triangle:
- c² = a² + b²
where c is the hypotenuse, and a and b are the other two sides (base and height). Here, we know:
- c = 25 cm (hypotenuse)
- a = 15 cm (base)
- b = ? (height)
Calculating the Height
Using the Pythagorean theorem:
- 25² = 15² + b²
- 625 = 225 + b²
- b² = 625 - 225
- b² = 400
- b = √400
- b = 20 cm (height)
Finding the Area
The area (A) of a right triangle can be calculated using the formula:
- A = (1/2) × base × height
- A = (1/2) × 15 cm × 20 cm
- A = (1/2) × 300 cm²
- A = 150 cm²
Conclusion
The area of the triangle is 150 cm². This process demonstrates the relationship between the sides of a right triangle and how to compute its area effectively.
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If the base of a right angle - triangle is 15 cm and it's hypotenuse is 25 find it's area?
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If the base of a right angle - triangle is 15 cm and it's hypotenuse is 25 find it's area? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the base of a right angle - triangle is 15 cm and it's hypotenuse is 25 find it's area? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the base of a right angle - triangle is 15 cm and it's hypotenuse is 25 find it's area?.
If the base of a right angle - triangle is 15 cm and it's hypotenuse is 25 find it's area? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the base of a right angle - triangle is 15 cm and it's hypotenuse is 25 find it's area? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the base of a right angle - triangle is 15 cm and it's hypotenuse is 25 find it's area?.
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