Calculate Side Length AC in Deltoid with Area 48 cm² and Diagonal 6 cm

To solve this problem, we'll follow these steps:

• Step 1: Use the formula for the area of a deltoid.

• Step 2: Substitute the known values into the formula.

• Step 3: Solve for the unknown diagonal $AC$.

Now, let's work through each step:

Step 1: The area of a deltoid is given by the formula:

$\text{Area} = \frac{1}{2} \times AC \times DB$

Step 2: Substitute the given values into the formula:

$48 = \frac{1}{2} \times AC \times 6$

Step 3: Solve for $AC$.

First, simplify the equation:

$48 = 3 \times AC$

Now, divide both sides by 3 to isolate $AC$:

$AC = \frac{48}{3} = 16$

Therefore, the solution to the problem is $AC = 16 \, \text{cm}$.