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One side other than the hypotenuse of right angle isosceles triangle is 6 cm. The length of the perpendicular on the hypotenuse from the opposite vertex is:
- a)6 cm
- b)6√2 cm
- c)4 cm
- d)3√2 cm
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
One side other than the hypotenuse of right angle isosceles triangle ...
Let ∠B be right angle in △ABC
and BD be perpendicular on hypotenuse AC then
1 / P2 = 1 / 62 + 1 / 62
P2 = 62 / 2 => p = 3√2.
Most Upvoted Answer
One side other than the hypotenuse of right angle isosceles triangle ...
Understanding Right-Angle Isosceles Triangle
In a right-angle isosceles triangle, two sides are equal, and the angles opposite these sides are both 45 degrees.
Given Measurements
- One side (leg) = 6 cm
- Both legs = 6 cm (since it's isosceles)
Finding the Hypotenuse
To find the hypotenuse (c) of this triangle, we can use the Pythagorean theorem:
- c = √(a² + b²)
- Here, a = 6 cm and b = 6 cm
Calculating:
- c = √(6² + 6²) = √(36 + 36) = √72 = 6√2 cm
Finding the Length of the Perpendicular
Now, to find the length of the perpendicular (h) from the opposite vertex to the hypotenuse, we can use the formula for the area of the triangle in two different ways.
1. Area using legs:
- Area = (1/2) × base × height = (1/2) × 6 × 6 = 18 cm²
2. Area using hypotenuse:
- The hypotenuse (base) = 6√2 cm
- Area = (1/2) × hypotenuse × height
- 18 = (1/2) × 6√2 × h
Now, we can solve for h:
- 18 = 3√2 × h
- h = 18 / (3√2) = 6 / √2 = 6√2 / 4 = 3√2 cm
Conclusion
Thus, the length of the perpendicular from the opposite vertex to the hypotenuse is 3√2 cm, confirming that option 'D' is correct.
In a right-angle isosceles triangle, two sides are equal, and the angles opposite these sides are both 45 degrees.
Given Measurements
- One side (leg) = 6 cm
- Both legs = 6 cm (since it's isosceles)
Finding the Hypotenuse
To find the hypotenuse (c) of this triangle, we can use the Pythagorean theorem:
- c = √(a² + b²)
- Here, a = 6 cm and b = 6 cm
Calculating:
- c = √(6² + 6²) = √(36 + 36) = √72 = 6√2 cm
Finding the Length of the Perpendicular
Now, to find the length of the perpendicular (h) from the opposite vertex to the hypotenuse, we can use the formula for the area of the triangle in two different ways.
1. Area using legs:
- Area = (1/2) × base × height = (1/2) × 6 × 6 = 18 cm²
2. Area using hypotenuse:
- The hypotenuse (base) = 6√2 cm
- Area = (1/2) × hypotenuse × height
- 18 = (1/2) × 6√2 × h
Now, we can solve for h:
- 18 = 3√2 × h
- h = 18 / (3√2) = 6 / √2 = 6√2 / 4 = 3√2 cm
Conclusion
Thus, the length of the perpendicular from the opposite vertex to the hypotenuse is 3√2 cm, confirming that option 'D' is correct.
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One side other than the hypotenuse of right angle isosceles triangle is 6 cm. The length of the perpendicular on the hypotenuse from the opposite vertex is:a)6 cmb)6√2 cmc)4 cmd)3√2 cmCorrect answer is option 'D'. Can you explain this answer?
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