Which of the following sets of sides form a triangle-2 cm- 3 cm- 5 cm3 cm- 4 cm- 5 cm1 cm- 1 cm- 2 cm3 cm- 4 cm- 8 cm

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Inequality Property of Triangles

Which of the ...

Question

Which of the following sets of sides form a triangle?

2 cm, 3 cm, 5 cm

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3 cm, 4 cm, 5 cm

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1 cm, 1 cm, 2 cm

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3 cm, 4 cm, 8 cm

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Solution

The correct option is B 3 cm, 4 cm, 5 cm
In a triangle, the sum of any two sides must always be greater than the third side.
a) 2 cm + 3 cm = 5 cm
b) 3 cm + 4 cm > 5 cm
c) 1 cm + 1 cm = 2 cm
d) 3 cm + 4 cm < 8 cm

$∴$ Only the set 3 cm, 4 cm, 5 cm follows "the sum of any two sides of a triangle is greater than the third side" criteria.
Thus, this set forms a triangle.

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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. Is it possible to construct a triangle with lengths of its sides as given below? Give reason for your answer.
(i) 5 cm, 4 cm, 9 cm
(ii) 8 cm, 7 cm, 4 cm
(iii) 10 cm, 5 cm, 6 cm
(iv) 2.5 cm, 5 cm, 7 cm
(v) 3 cm, 4 cm, 8 cm

Q. Which of the following is the set of measures of the sides of a triangle?
(a) 8 cm, 4 cm, 20 cm
(b) 9 cm, 17 cm, 25 cm
(c) 11 cm, 16 cm, 28 cm
(d) None of these

Which of the following sets of side lengths will form a triangle?

$3$ cm, $1.3$ cm, $5$ cm.

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