Q. 44.0( 128 Votes )

# Which of the following can be the sides of a right triangle?

(i) 2.5 cm, 6.5 cm, 6 cm.

(ii) 2 cm, 2 cm, 5 cm.

(iii) 1.5 cm, 2 cm, 2.5 cm.

In the case of right-angled triangles, identify the right angles.

Answer :

**(i)** In the given question, we have to identify the right angles

It is given in the question that,

Sides of triangle = 2.5 cm, 6.5 cm and 6 cm

(2.5)^{2} = 6.25

(6.5)^{2} = 42.25

(6)^{2} = 36

Now, it can be observed that,

36 + 6.25 = 42.25

(6)^{2} + (2.5)^{2} = (6.5)^{2}

∴ The square of the length of one side of the triangle is the sum of the squares of other two sides

Hence,

These are the sides of the right angled triangle

The right angle of the triangle will be in the front of the side 6.5 cm

**(ii)** In the given question, we have to identify the right angles

It is given in the question that,

Sides of triangle = 2 cm, 2 cm and 5 cm

(2)^{2} = 4

(2)^{2} = 4

(5)^{2} = 25

Now, it can be observed that,

(2)^{2} + (2)^{2} (5)^{2}

∴ The square of the length of one side of the triangle is not equal to the sum of the squares of other two sides

Hence,

These are not the sides of the right angled triangle

**(iii)** In the given question, we have to identify the right angles

It is given in the question that,

Sides of triangle = 1.5 cm, 2 cm and 2.5 cm

(1.5)^{2} = 2.25

(2)^{2} = 4

2.5)^{2} = 6.25

Now, it can be observed that,

2.25 + 4 = 6.25

Hence,

(1.5)^{2} + (2)^{2} = (2.5)^{2}

∴ The square of the length of one side of the triangle is the sum of the squares of other two sides

Hence,

These are the sides of the right angled triangle

The right angle of the triangle will be in the front of the side 2.5 cm

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