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If the sides of a right triangle are 9 cm and 12 cm, its hypotenuse is:
- a)13 cm
- b)15 cm
- c)18 cm
- d)21 cm
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If the sides of a right triangle are 9 cm and 12 cm, its hypotenuse is...
Understanding Right Triangles
In a right triangle, the sides can be described using the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Given Values
- One side (a) = 9 cm
- Other side (b) = 12 cm
Applying the Pythagorean Theorem
To find the length of the hypotenuse (c), we can use the formula:
c² = a² + b²
Substituting the values:
- c² = (9 cm)² + (12 cm)²
- c² = 81 cm² + 144 cm²
- c² = 225 cm²
Calculating the Hypotenuse
Now, take the square root of both sides to find c:
- c = √(225 cm²)
- c = 15 cm
Conclusion
Thus, the hypotenuse of the triangle is 15 cm, confirming that the correct answer is option 'B'.
Understanding these calculations is essential for solving problems related to right triangles in geometry.
In a right triangle, the sides can be described using the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Given Values
- One side (a) = 9 cm
- Other side (b) = 12 cm
Applying the Pythagorean Theorem
To find the length of the hypotenuse (c), we can use the formula:
c² = a² + b²
Substituting the values:
- c² = (9 cm)² + (12 cm)²
- c² = 81 cm² + 144 cm²
- c² = 225 cm²
Calculating the Hypotenuse
Now, take the square root of both sides to find c:
- c = √(225 cm²)
- c = 15 cm
Conclusion
Thus, the hypotenuse of the triangle is 15 cm, confirming that the correct answer is option 'B'.
Understanding these calculations is essential for solving problems related to right triangles in geometry.
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Community Answer
If the sides of a right triangle are 9 cm and 12 cm, its hypotenuse is...
Use the Pythagorean theorem: c = √(a2 + b2).
Compute: 92 = 81 and 122 = 144.
Sum = 81 + 144 = 225, so c = √225 = 15 cm.
Answer: 15 cm (option B).
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