Calculate the Diagonal DB in a Deltoid with Area 63 cm² and AC = 7

To solve the problem, we will apply the formula for the area of a deltoid using its diagonals.

The formula for the area $A$ of a deltoid with diagonals $p$ and $q$ is given by:

$A = \frac{1}{2} \times p \times q$

where $p$ and $q$ are the lengths of diagonals AC and DB, respectively.

In this problem:

• Diagonal $p = AC = 7$ cm
• The area $A = 63$ cm²

We need to find diagonal $q = DB$.

Substituting the known values into the formula:

$63 = \frac{1}{2} \times 7 \times DB$

To isolate $DB$, first multiply both sides by 2:

$126 = 7 \times DB$

Now, divide both sides by 7 to solve for $DB$:

$DB = \frac{126}{7}$

Calculating this gives:

$DB = 18$

Therefore, the length of diagonal $DB$ is 18 cm.