Question:
What is the length of the hypotenuse of a right triangle with legs of lengths 5 and 12 units?
What is the length of the hypotenuse of a right triangle with legs of lengths 5 and 12 units?
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Memorizing common Pythagorean triples can save a lot of time in exams. The most common ones are (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25), along with their multiples (e.g., 6, 8, 10).
Updated On: Oct 4, 2025
- 13 units
- 14 units
- 15 units
- 17 units
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept
This question involves a right-angled triangle. The side opposite the right angle is called the hypotenuse, and it is the longest side. The other two sides are called legs. The relationship between the lengths of the sides is described by the Pythagorean theorem.
Step 2: Key Formula or Approach
The Pythagorean theorem states that in a right triangle with legs 'a' and 'b' and hypotenuse 'c':
\[ a^2 + b^2 = c^2 \] Step 3: Detailed Explanation
We are given the lengths of the two legs:
a = 5 units
b = 12 units
We need to find the length of the hypotenuse, c.
Substitute the given values into the theorem:
\[ 5^2 + 12^2 = c^2 \] \[ 25 + 144 = c^2 \] \[ 169 = c^2 \] To find 'c', take the square root of both sides:
\[ c = \sqrt{169} \] \[ c = 13 \text{ units} \] Step 4: Final Answer
The length of the hypotenuse is 13 units.
This question involves a right-angled triangle. The side opposite the right angle is called the hypotenuse, and it is the longest side. The other two sides are called legs. The relationship between the lengths of the sides is described by the Pythagorean theorem.
Step 2: Key Formula or Approach
The Pythagorean theorem states that in a right triangle with legs 'a' and 'b' and hypotenuse 'c':
\[ a^2 + b^2 = c^2 \] Step 3: Detailed Explanation
We are given the lengths of the two legs:
a = 5 units
b = 12 units
We need to find the length of the hypotenuse, c.
Substitute the given values into the theorem:
\[ 5^2 + 12^2 = c^2 \] \[ 25 + 144 = c^2 \] \[ 169 = c^2 \] To find 'c', take the square root of both sides:
\[ c = \sqrt{169} \] \[ c = 13 \text{ units} \] Step 4: Final Answer
The length of the hypotenuse is 13 units.
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