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If the two legs of a right angled triangle are equal and the square of the hypotenuse is 100 sq units, what is the length of each leg?
- a)10 units
- b)5√2 units
- c)10√2 units
- d)15 units
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If the two legs of a right angled triangle are equal and the square of...
Let's solve the problem step by step:
Given:
- The two legs of a right-angled triangle are equal.
- The square of the hypotenuse is 100 square units.
Let the length of each leg be x units.
Using the Pythagorean theorem:
Most Upvoted Answer
If the two legs of a right angled triangle are equal and the square of...
Understanding the Right-Angled Triangle
In a right-angled triangle, if the two legs are equal, we can refer to them as 'x'. According to the Pythagorean theorem, the relationship between the legs and the hypotenuse is given by:
- Hypotenuse² = Leg₁² + Leg₂²
Since both legs are equal:
- Hypotenuse² = x² + x²
- Hypotenuse² = 2x²
Given Information
We know that the square of the hypotenuse is 100 square units:
- 2x² = 100
Solving for x
To find the length of each leg, follow these steps:
1. Divide both sides by 2:
- x² = 100 / 2
- x² = 50
2. Now, take the square root of both sides to find 'x':
- x = √50
- x = √(25 * 2)
- x = 5√2
Conclusion
Thus, the length of each leg of the triangle is 5√2 units. Therefore, the correct answer is:
Option 'B': 5√2 units
In a right-angled triangle, if the two legs are equal, we can refer to them as 'x'. According to the Pythagorean theorem, the relationship between the legs and the hypotenuse is given by:
- Hypotenuse² = Leg₁² + Leg₂²
Since both legs are equal:
- Hypotenuse² = x² + x²
- Hypotenuse² = 2x²
Given Information
We know that the square of the hypotenuse is 100 square units:
- 2x² = 100
Solving for x
To find the length of each leg, follow these steps:
1. Divide both sides by 2:
- x² = 100 / 2
- x² = 50
2. Now, take the square root of both sides to find 'x':
- x = √50
- x = √(25 * 2)
- x = 5√2
Conclusion
Thus, the length of each leg of the triangle is 5√2 units. Therefore, the correct answer is:
Option 'B': 5√2 units
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