Question

Q - which of the following can be the sides of a right triangle ?

1) 2.5cm, 6.5cm, 6cm

2) 2cm, 2cm, 5cm

3) 1.5cm, 2cm, 2.5 cm


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Answer 1

In a right angle triangle square of largest side is equal to the sum of squares of two smaller side

Now,

Applying this statement in above three measurements...

1) 2.5cm, 6.5cm, 6cm

(6.5)² = (2.5)² + (6)²

42.25 = 6.25 + 36

42.25 = 42.25

It is equal so that it is possible

2) 2cm, 2cm, 5cm

(5)² = (2)² + (2)²

25 = 4 + 4

25 = 8

It is not equal so that it is

Not possible

3) 1.5cm, 2cm, 2.5 cm

(2.5)² = (2)² + (1.5)²

6.25 = 4 + 2.25

6.25 = 6.25

It is equal so that it is possible

Yes , the 1st and 3rd one can be the sides of a right triangle

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Answer 2

Answer:

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☆As we know that in a right angled triangle, the square of longest ( hypotenuse) is equal to sum of squares of other two side.

______________________________________

1) Let a = 2.5, b= 6.5, c = 6m.

$a {}^{2} + c{}^{2} = (2.5) {}^{2} + (6) {}^{2} cm {}^{2} \\ \\ (6.25 +36)cm {}^{2} \\ \\ \\ a { }^{2} + c { }^{2} = 42.25cm {}^{2}$

$\boxed{Now}$

$b {}^{2} = (6.5) { }^{2} = 6.5 \times 6.5 = 42.25cm {}^{2} \\ \\ = > a { }^{2} + c { }^{2} = b {}^{2} \\ \\ 2.5cm. \: \: 6cm \: 6.5cm \: are \: the \: sides \: of \: the \: right \: anged \: triangle.$

2) Let a = 2 ,b = 2 ,c = 5.

$a {}^{2} + b {}^{2} = (2) {}^{2} + (2) {}^{2} = 4 + 4 \\ \\ a {}^{2} + b {}^{2} = 8 \\ \\ c {}^{2} = (5) {}^{2} = 25 \\ \\ a {}^{2} + b {}^{2} \: is \: not \: equal \: to \: c {}^{2}$

=> 2 cm , 2 cm and 5 cm are not the sides of triangle.

3) let a = 1.5 ,b = 2cm ,c =2.5 cm.

$a {}^{2} + b {}^{2} = (1.5) {}^{2} + (2) {}^{2} \\ \\ = 2.25 + 4 = 6.25 \\ \\ c {}^{2} = (2.5) {}^{2} \\ \\ = 6.25 \\ \\ a {}^{2} + b { }^{2} = c {}^{2}$

$\huge\boxed{3rd\:option\:and\:1st\:option\:is\:correct}$