Question

The sides of a triangle are 7, 4, n. If n is an integer, state the largest and smallest possible values of n.

Answer 1

Smallest value of n = 4

Largest value of n = 10

Explanation:

The sum of the shortest sides of a triangle must be greater than the longest side.

If 7 is the longest side, then:

n + 4 > 7

n > 3

n is an integer, so the smallest n can be is 4.

If n is the longest side, then:

4 + 7 > n

11 > n

n is an integer, so the largest n can be is 10.

Answer 2

4, 10

Explanation:

The value for the third side of the triangle is given by

b-a < n < b+a where a and b are the two other sides of the triangle and b>a

7-4 < n < 7+4

3 < n < 11

Since n is an integer

4 would be the smallest value and 10 would be the largest