Question

Which one of the following number triplet cannot represent the length units of the sides of a triangle?
a) (5, 2, 2)
(b) (3, 4, 5)
(C) (5, 12, 13)
(d) (4, 7, 8)
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Answer 1

Answer:

hypotenuse is the longest side

hypotenuse ²=side1²+side2²

a)5,2,2

5²=2²+2²

25 is not equal to 8

therefore, it is not a triangle

b)3,4,5

5²=3²+4²

25=9+16

25=25

therefore, it is right angled triangle

c)5,12,13

13²=5²+12²

169=25+144

169=169

therefore, it is a right angled triangle

d)4,7,8

8²=4²+7²

64=16+49

64 is not equal to 65

therefore, it is not a right angled triangle

Answer 2

Answer:

(a) (5,2,2)

Sol: We know that ,

The sum of the lengths of any two sides of a triangle is

greater than third side.Here, 5cm+2cm =7 cm > 2cm

2cm + 2cm = 4cm < 5cm

So ,

The triangle with sides 5cm ,2cm and 2cm is not

possible.

(b) (3,4,5)

Sol: We know that ,

The sum of the lengths of any two sides of a triangle is

greater than third side.

Here, 3cm+4cm =7 cm > 5cm

4cm + 5cm = 9cm > 3cm

5cm + 3cm = 8cm >4cm

So ,

The triangle with sides 3cm ,4cm and 5cm is possible.