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Which of the following will form the sides of a triangle?

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23 cm, 17 cm, 8 cm

12 cm, 10 cm, 25 cm

6 cm, 7 cm, 16 cm

8 cm, 7 cm, 16 cm

answer is A.

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Detailed Solution

We have to choose a combination of sides of triangle.
We know that, according to the triangle inequality theorem, the sum of a triangle's two sides is always greater than its third side.

(1) 17 + 8 > 23

is true.
Hence, the sides with the measure

23 cm, 17 cm, 8 cm

will form the sides of a triangle.

(2) 10 + 12 > 25

is not true.
Hence, the sides with the measure

10 cm, 12 cm, 25 cm

will not form the sides of a triangle.

(3) 6 + 7 > 16

is not true.
Hence, the sides with the measure

6 cm, 7 cm, 16 cm

will not form the sides of a triangle.

(4) 8 + 7 > 16

is not true.
Hence, the sides with the measure

8 cm, 7 cm, 16 cm

will not form the sides of a triangle.
Hence, option 1 is correct.

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Which of the following will form the sides of a triangle?

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