Calculate Side Length AC in a Deltoid with Area 45 cm² and DB = 9

To solve this problem, follow these steps:

• Step 1: Identify the given information
• Step 2: Use the formula for the area of a deltoid
• Step 3: Perform the algebraic solution

Let's work through each step:

Step 1: We know that $DB = 9$ cm and the area $S = 45$ cm². We are asked to find $AC$.

Step 2: The formula for the area of a deltoid is $S = \frac{1}{2} \times d_1 \times d_2$. Here, $d_1 = AC$ and $d_2 = DB = 9$.

Step 3: Substitute the known values into the formula:
$45 = \frac{1}{2} \times AC \times 9$
$45 = \frac{9}{2} \times AC$
Multiply both sides by 2 to eliminate the fraction:
$90 = 9 \times AC$
Divide both sides by 9 to solve for $AC$:
$AC = \frac{90}{9}$
$AC = 10$ cm.

Therefore, the length of side $AC$ is 10 cm.