Question

Find hypotenuse of isosceles triangle having congruent side a cm. .​

Answer 1

Answer:

1. 102 cm. B.
2. 5 cm. C.
3. 2 cm. D.

32 cm. MEDIUM. Answer. In an isosceles right angled triangle, the two sides on the right angle are equal . Hence, hypotenuse of the isosceles right angled triangle of side a=a2+a2 =2 a. Hence, length of hypotenuse =2 ×10=102. Answered By. toppr. How satisfied are you with the answer?

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Answer 2

Complete Question:

In an isosceles right angled triangle, one of the congruent sides is of length 10 cm. Find the length of the altitude on the hypotenuse.

Answer:

Hence, length of hypotenuse = $10\sqrt{2}$

Explanation:

Given:

The triangle is isosceles right-angled

Congruent side = 10 cm

To Find:

Length of the altitude on the hypotenuse

Concept:

Triangles

Solution:
The two sides of the right angle are equal in an isosceles right angled triangle.

Let the isosceles right angled triangle of side be a

Formula:

$H^{2} = P^{2} +B^{2}$

Therefore, $H= \sqrt{a^{2} +a^{2} }$

$H=a\sqrt{2}$

Thus the length of the hypotenuse is $10*\sqrt{2} =10\sqrt{2}$

Conclusion:

The length of the altitude on the hypotenuse is $10\sqrt{2}$

Definition:

Hypotenuse:

• The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry.
• The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, may be used to determine the length of the hypotenuse.
• In this case, if one of the other sides is 3 (when squared, 9) and the other is 4 (when squared, 16), then the sum of their squares is 25. the square root of 25, or 5, is the length of the hypotenuse.

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