Deltoid Area Problem: Finding AC Length Given Area of 49 cm²

To solve for the length of side AC in the deltoid:

• Step 1: Identify the formula for the area, which is given by:
  $\text{Area} = \frac{1}{2} \times BD \times AC$ where $BD$ and $AC$ are the diagonals.
• Step 2: Substitute known values into the formula:
  Given that $BD = 7\, \text{cm}$ and $\text{Area} = 49\, \text{cm}^2$, we have:
  $49 = \frac{1}{2} \times 7 \times AC$
• Step 3: Solve the equation for $AC$:
  Multiply both sides of the equation by 2 to eliminate the fraction:
  $98 = 7 \times AC$ Divide both sides by 7:
  $AC = \frac{98}{7} = 14$

Therefore, the length of the side $AC$ is $14 \, \text{cm}$.