In ΔABC, if AB = 14 and BC = 9, AC may be equal to

AC could be any number of these numbers 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22

Step-by-step explanation:

There is a fact in any triangle:

The length of any side of a triangle must be greater than the difference of the lengths of the other two sides and smaller than the sum of the lengths of the other two sides

If the lengths of the three sides of a triangle are a, b and c, then

a - b < c < a + b b - c < a < b + c a - c < b < a + c

In Δ ABC:

→ (BC) - (AC) < AB < (BC) + (AC)

→ (AB) - (AC) < BC < (AB) + (AC)

→ (AB) - (BC) < AC < (AB) + (BC)

∵ AB = 14 units

∵ BC = 9 units

- Find the sum and difference of them

∵ AB - BC = 14 - 9

∴ AB - BC = 5

∵ AB + BC = 14 + 9

∴ AB + BC = 23

- That means the length of AC could be any integer greater

than 5 and smaller than 23

∴ 5 < AC < 23

AC could be any number of these numbers 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22