Question

A triangle is given whose sides are of length 21 cm, 20 cm and 29 cm. Check whether these are the sides of a right-angled triangle.​

Answer 1

We can use the Pythagorean theorem to check whether the sides (21 cm, 20 cm, and 29 cm) form a right-angled triangle. According to the Pythagorean theorem, in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the courts of the other two sides.

Let's denote the sides as follows:

a = 21 cm (one side)

b = 20 cm (another side)

c = 29 cm (hypotenuse)

The Pythagorean theorem can be written as:

c² = a² + b²

Substitute the given values:

29² = 21² + 20²

841 = 441 + 400

Since 841 is equal to 841, the Pythagorean theorem is satisfied.

Now, we need to determine if this is a right-angled triangle. For a triangle to be right-angled, the Pythagorean theorem must hold, and the sum of the squares of the two shorter sides must be equal to the court of the longest side (hypotenuse).

Let's check if it satisfies the right-angle condition:

If 29² = 21² + 20², then the triangle is right-angled.

29² = 841

21² + 20² = 441 + 400 = 841

Since both sides are equal, the given sides (21 cm, 20 cm, and 29 cm) form a right-angled triangle.

Therefore, the given sides do form a right-angled triangle.

Answer 2

Yes, the triangle is a right-angled triangle.

Explanation:

Given:

• The sides of the triangle are 21 cm, 20 cm and 29 cm.

To find:

• Whether the triangle is a right-angled triangle.

Solution:

We can use the Pythagoras theorem to check whether the triangle is a right-angled triangle.

Pythagorean theorem:

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is the longest side, which is 29 cm.

The other two sides are 21 cm and 20 cm.

`\sf 29^2= 21^2+ 20^2`

`\sf 841 = 441 + 400`

`\sf 841 = 841`

Since the square of the hypotenuse is equal to the sum of the squares of the other two sides, the triangle is a right-angled triangle.