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Question
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 ______.
Options
3.6 cm
4.1 cm
3.8 cm
3.4 cm
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Solution
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 3.4 cm.
Explanation:
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 cm
We 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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