Question

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

1.  2.5 cm, 6.5 cm, 6 cm 
2.  2 cm, 2 cm, 5 cm 
3.  1.5 cm, 2 cm, 2.5 cm 

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

Answer 1

(i) \(2.5\) cm, \(6.5\) cm, \(6\) cm
\((2.5)^2= 6.25\)
\((6.5)^2= 42.25\)
\((6)^2= 36\)
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 is the sum of the squares of the lengths of the remaining two sides. 
Hence, these are the sides of a right-angled triangle. Right angle will be in front of the side of \(6.5 \) \(cm\) measure. 

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(ii) \(2\) \(cm\), \(2\) \(cm\), \(5\) \(cm\)
\((2)^2= 4\)
\((2)^2= 4\)
\((5)^2= 25\)
Here, \((2)^2+ (2)^2 ≠ (5)^2\)

The square of the length of one side is not equal to the sum of the squares of the lengths of the remaining two sides. 
Hence, these sides are not of a right-angled triangle.

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(iii) \(1.5\) cm, \(2\) \(cm\), \(2.5\) \(cm\)
\((1.5)^2= 2.25\)
\((2)^2= 4\)
\((2.5)^2= 6.25\)
Here,
\(2.25 + 4 = 6.25\)
\((1.5)^2+ (2)^2= (2.5)^2\)

The square of the length of one side is the sum of the squares of the lengths of the remaining two sides. 
Hence, these are the sides of a right-angled triangle. 
Right angle will be in front of the side of \(2.5\) \(cm\) measure.