Deltoid Geometry: Finding Side Length AC Given Area 60cm² and BD=15cm

To solve this problem, we'll apply the following steps:

• Step 1: Identify the given information: $BD = 15$ cm and the area is $60$ cm².

• Step 2: Use the formula for the area of a deltoid.

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

Now, let's work through each step:
Step 1: We know the area formula for a deltoid is given by: $\text{Area} = \frac{1}{2} \times AC \times BD$

Step 2: Substitute the given values into the formula: $60 = \frac{1}{2} \times AC \times 15$

Step 3: Simplify and solve for $AC$: $60 = \frac{15}{2} \times AC$
Multiply both sides by 2 to isolate $AC$: $120 = 15 \times AC$
Divide both sides by 15: $AC = \frac{120}{15} = 8$

Therefore, the length of the side $AC$ is $8$ cm.