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Q.

If the length of the largest side of a triangle is 12 cm, then the other two sides can be


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a

4.8 cm, 8.2 cm  

b

3.2 cm, 7.8 cm  

c

6.4 cm, 2.8 cm  

d

7.6 cm, 3.4 cm   

answer is A.

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Detailed Solution

It is given that the length of the largest side of a triangle is 12 cm.
We need to find which of the given pairs can be the other two sides of the triangle.
The triangle inequality theorem states that “The sum of the lengths of any two sides of a triangle is greater than the length of the third side”.
Here, the sum of other two sides must be greater than 12  cm.
From option 1, we have,
4.8  cm+8.2  cm=13  cm
⇒13  cm>12  cm
From option 2, we have,
3.2  cm+7.8  cm=11  cm
⇒11  cm<12  cm
From option 3, we have,
6.4  cm+2.8  cm=9.2  cm
⇒9.2  cm<12  cm
From option 4, we have,
7.6  cm+3.4  cm=11  cm
⇒11 cm<12  cm
Therefore, the other two sides of the triangle can be 4.8 cm and 8.2 cm.
Hence, option (1) is correct.
 
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If the length of the largest side of a triangle is 12 cm, then the other two sides can be