Atriangle has two sides of length 20 and 2. what is the smallest possible whole-number length for the third side?

The smallest possible whole-number length for the third side is 19.

Given the following data:

To calculate the smallest possible whole-number length for the third side of the triangle:

In Mathematics, the sum of any two sides of a triangle must be greater than the third side of the triangle.

Thus,

In conclusion, the smallest possible whole-number length for the third side is 19.

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a, b, c - sides of a triangle

a + b > c

a + c > b

b + c > a

We have a = 20 and b = 2. Substitute:

20 + 2 > c

22 > c → c < 22

20 + c > 2      subtract 20 from both sides

c > -18

2 + c > 20          subtract 2 from both sides

c > 18

c < 22 and c > -18 and c > 18

Therefore 18 < c < 22.

The smallest possible whole number length of third side is 19.

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