Find the Side Length BD in a Deltoid with Area 48 cm² and AC = 6 cm

To solve for $BD$, the diagonal of the deltoid, follow these steps:

• Step 1: Recognize that the area of a deltoid with perpendicular diagonals is given by the formula $A = \frac{1}{2} \times d_1 \times d_2$.
• Step 2: Substitute the known values into the formula: $48 = \frac{1}{2} \times 6 \times BD$.
• Step 3: Simplify and solve for $BD$:

Substituting $AC = 6$ cm, we have:

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

Multiply both sides by 2 to clear the fraction:

$96 = 6 \times BD$

Divide both sides by 6 to solve for $BD$:

$BD = \frac{96}{6} = 16$ cm

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