Question

What is the smallest whole number larger than the perimeter of any triangle with a side of length 5 and a side of length 19?

Answer 1

The smallest whole number larger than the perimeter of the given triangle is 52.

Step-by-step explanation:

To find the perimeter of a triangle, we add the lengths of all three sides. In this case, we have two sides of length 5 and 19. The third side is unknown, but it must be longer than the difference between the other two sides and shorter than the sum of the other two sides. So, the smallest whole number larger than the perimeter of this triangle would be the sum of the two given sides plus the difference between the two given sides: 5 + 19 + (19 - 5) = 5 + 19 + 14 = 38 + 14 = 52.

Answer 2

39

Step-by-step explanation:

In a triangle, the sum of any two side lengths must exceed the length of the remaining third side. Therefore these 3 inequalities must be true.

5 + 19 > x

5 + x > 19

19 + x > 5

We can ignore the third inequality because, for any positive value of x, the inequality is true.

x < 26

x > 14

Now we know that x, the length of the third side, must be greater than 14 but less than 26. Since we are asked for the smallest whole number possible, the third side would be length 15. Therefore the perimeter is 5 + 19 + 15 = 39.