Ram wants to fence his triangular garden. If two of the sides measure 5 feet and 7 feet, then which of the following is a possible option for the length of the third side?

10 feet

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12 feet

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13 feet

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15 feet

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Solution

The correct option is A 10 feet
The sum of any two sides of triangle should be greater than the third side.
If we consider the first option, this condition holds as shown below:
5 feet + 7 feet = 12 feet $>$ 10 feet
5 feet + 10 feet = 15 feet $>$ 7 feet
10 feet + 7 feet = 17 feet $>$ 5 feet
But, if we consider the triplet 5 feet, 7 feet and 12 feet, since
5 feet + 7 feet = 12 feet $≯$ 12 feet.
Similarly, we can rule out the other options.

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