Answer:
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:
<em>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</em>
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
