Calculate Triangle Side AC and Height AE: Given Area 56 cm² and Side 4⅔ cm

Let's solve the problem using the information given:

• We know the area of triangle $ABC$ is given by the formula: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$.
• For calculating $AE$, use the entire base $BC$ which is $4 \frac{2}{3} \, \text{cm}$. Convert this to an improper fraction: $BC = \frac{14}{3} \, \text{cm}$.
• Plug into the area formula: $56 = \frac{1}{2} \times \frac{14}{3} \times AE$.
• Solve for $AE$: $AE = \frac{56 \times 2 \times 3}{14} = 24 \, \text{cm}$.
• For calculating $AC$, use base $BD$: $\text{Area} = \frac{1}{2} \times AC \times BD$.
• Substitute known values: $56 = \frac{1}{2} \times AC \times 7$.
• Solve for $AC$: $AC = \frac{56 \times 2}{7} = 16 \, \text{cm}$.

Therefore, the lengths are $AC = 16 \, \text{cm}$ and $AE = 24 \, \text{cm}$.

The correct choice is option 2:
AC = 16
AE = 24