Vi if two sides of a triangles are 5cm and 1.5 cm the length of its third side cannot be

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(d) Given, the length of two sides of a triangle are 5 cm and 1.5 cm, respectively.Let sides AB = 5 cm and CA = 1.5 cmWe know that, a closed figure formed by three intersecting lines (or sides) is called a triangle, if difference of two sides < third side and sum of two sides > third side∴ 5-1.5 < BC and 5+1.5 > BC ⇒ 3.5 < BC and 6.5 > BC

Here, we see that options (a), (b) and (c) satisfy the above inequality but option (d) does not satisfy the above inequality.

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Choose the correct alternative answer for the following question.

If two sides of a triangle are 5 cm and 1.5 cm, the length of its third side cannot be __________

• 3.7 cm

• 4.1 cm

• 3.8 cm

•  3.4 cm

According to the triangle inequality, "the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side".Therefore, the length of the third side cannot be greater than 3.4 cm.

Hence, the correct answer is 3.4 cm.

Concept: Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle

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