Which of the following given nbsp-lengths can be the sides of a triangle-3 cm- 4 cm- 5 cm-1 cm- 2 cm- 3 cm-4 cm- 2 cm- 1 nbsp-cm-2 cm- 4 cm- 6 cm-

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Standard IX

Mathematics

Which of the ...

Question

Which of the following given lengths can be the sides of a triangle?

3 cm, 4 cm, 5 cm

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1 cm, 2 cm, 3 cm

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2 cm, 4 cm, 6 cm

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4 cm, 2 cm, 1 cm

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Solution

The correct option is A
3 cm, 4 cm, 5 cm

For a geometrical figure to be a triangle, the sum of lengths of any two of its sides must be greater than that of the third side.

Otherwise, a triangle formation is not possible.
The only option among the given options which satisfies the above condition is '3 cm, 4 cm, 5 cm'.
[3 cm + 4 cm > 5 cm
4 cm + 5 cm > 3 cm
5 cm + 3 cm > 4 cm]

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Similar questions

Suppose we want to draw a triangle with one side 6 centimeters long. Which of the following pairs of lengths can be the lengths of the other two sides?

(i) 4 cm, 1 cm

(ii) 4 cm, 2 cm

(iii) 4 cm, 3 cm

(iv) 5 cm, 10 cm

(v) 5 cm, 11 cm

(vi) 5 cm, 12 cm

Q. The lengths of the sides of some triangles are given. Say what types of triangles they are.
(1) 3 cm, 4 cm, 5 cm (2) 3.4 cm, 3.4 cm, 5 cm
(3) 4.3 cm, 4.3 cm, 4.3 cm (4) 3.7 cm, 3.4 cm, 4 cm

Q. The lengths of three segments are given for constructing a triangle. Say whether a triangle with these sides can be drawn. Give the reason for your answer.
(1) 17 cm, 7 cm, 8 cm (2) 7 cm, 24 cm, 25 cm
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Q. Is it possible to draw a triangle, the lengths of whose sides are given below?

(i) 1 cm, 1 cm, 1 cm
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(iii) 7 cm, 8 cm, 15 cm
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Q. Is it possible to construct a triangle with lengths of its sides as given below? Give reason for your answer.
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(iv) 2.5 cm, 5 cm, 7 cm
(v) 3 cm, 4 cm, 8 cm

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Standard IX Mathematics

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