Deltoid Geometry: Find BD Length Given AC=9cm and Area=72cm²

To solve this problem, we will compute the length of diagonal BD using the formula for the area of a deltoid:

• Step 1: Recall the formula for the area of a deltoid, which is given by:
$\text{Area} = \frac{1}{2} \times AC \times BD$
• Step 2: Substitute the known values into the formula:
$72 = \frac{1}{2} \times 9 \times BD$
• Step 3: Solve the equation for BD:

First, multiply both sides of the equation by 2 to clear the fraction:

$144 = 9 \times BD$

Next, divide both sides by 9 to isolate BD:

$BD = \frac{144}{9}$
• Step 4: Perform the division:
$BD = 16$

Thus, the length of diagonal BD is $16$ cm.

This conclusion matches the possible answer choice 4:

The correct choice is (4): $16$ cm.