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  • Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be (A) 3.6 cm (B) 4.1 cm (C) 3.8 cm (D) 3.4 cm

Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be

(A) 3.6 cm

(B) 4.1 cm

(C) 3.8 cm

(D) 3.4 cm

Answers (1)

[D]

Solution.         We know that, sum of two sides of a triangle is greater than the third side.

(A) BC = 1.5 cm, AC = 3.6 cm (Assume)

Then, BC + AC = 1.5 + 3.6 cm = 5.1 cm

Sum of two side BC and AC is more than third side AB = 5 cm

Therefore, AC = 3.6 cm is possible.

(B) BC = 1.5 cm, AC = 4.1 cm (Assume)

Then, BC + AC = 1.5 + 4.1 cm = 5.6 cm

Sum of two side BC and AC is more than third side AB = 5 cm

Therefore, AC = 4.1 cm is possible.

(C) BC = 1.5 cm, AC = 3.8 cm (Assume)

Then, BC + AC = 1.5 + 3.8 cm = 5.3 cm

Sum of two side BC and AC is more than third side AB = 5 cm

Therefore, AC = 3.8 cm is possible.

(D) BC = 1.5 cm, AC = 3.4 cm (Assume)

Then, BC + AC = 1.5 + 3.4 cm = 4.9 cm

Sum of two side BC and AC is less than third side AB = 5 cm

Therefore, AC = 3.4 cm cannot be possible.

Hence option (D) is correct.

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