Calculate Deltoid Dimensions: Finding DB When AC = 2X and Area = 32 cm²

Shown below is the deltoid ABCD.

AC = 2X

DB = X

The area of the deltoid is equal to 32 cm².

Calculate DB.

Video Solution

Solution Steps

00:11 Let's start by calculating the diagonal D to B.

00:15 We'll use the formula for finding a rhombus's area.

00:20 That's diagonal one times diagonal two, divided by two.

00:25 Let's substitute the given values to find diagonal D to B.

00:33 Then, multiply by two to remove the fraction.

00:43 Next, we'll isolate the variable X.

00:56 And that's how we solve this problem!

Step-by-Step Solution

To solve this problem, we will utilize the formula for the area of a deltoid, which is $\frac{1}{2} \times AC \times DB$ . Given:

The formula for the area of the deltoid is:

$\text{Area} = \frac{1}{2} \times AC \times DB$

Substitute the given values into the formula:

$32 = \frac{1}{2} \times 2X \times X$

Simplify the equation:

$32 = \frac{1}{2} \times 2X^2$

$32 = X^2$

Solve for $X$ by taking the square root of both sides:

$X = \sqrt{32}$

Since $DB = X$ , the length of diagonal $DB$ is $\sqrt{32}$ .

Thus, the solution to the problem is $\sqrt{32}$ .