Question

Two of the three sides of a triangle are 20 and 15. Which of the following numbers is not a possible perimeter of the triangle?

a. 52
b. 57
c. 62
d. 67 e.72

Answer 1

Given:
1st side = 15
2nd side = 20
3rd side = ?

We will use a triangle inequality where the 3rd side is greater than the difference of the two sides and less than the sum of the two sides.

20 - 15 < x < 20 + 15
5 < x < 35

If x = 5 ; then the perimeter would be 5 + 15 + 20 = 40
if x = 35, then the perimeter would be 35 + 15 + 20 = 70

So the perimeter is within the range of 40 and 70.

Among the choices, E. 72 is outside the range. Therefore, it is not a possible perimeter of the triangle.