Area of quad = 20cm sq1/2×sum of offsets×Diagonal BD=201/2 × 5cm × BD = 20cm sqso,BD=8 cm

Problem:
The total area of a quadrilateral ABCD is 20 cm². The offsets BD are 2 cm and 3 cm. What is the length of BD?

Solution:

To find the length of BD, we need to apply the formula for the area of a quadrilateral. The formula for the area of a quadrilateral can be calculated using the lengths of its sides and the offsets. Let's break down the solution into the following steps:

Step 1: Identify the given information:
- Total area of the quadrilateral ABCD = 20 cm².
- BD offsets = 2 cm and 3 cm.

Step 2: Understand the concept of offsets:
In a quadrilateral, offsets are the perpendicular distances between opposite sides. In this case, BD is one of the sides, and the offsets are given as 2 cm and 3 cm. These offsets help in calculating the area of the quadrilateral.

Step 3: Calculate the area of the quadrilateral:
The area of a quadrilateral can be calculated by multiplying the lengths of the offsets by the length of the side they are offset from and taking the square root of the product. For this problem, we have two offsets, so the area can be calculated as follows:

Area = √(offset1 * offset2 * BD)

Step 4: Substitute the given values into the formula:
Area = √(2 cm * 3 cm * BD)

Step 5: Simplify the expression and solve for BD:
20 cm² = √(6 cm² * BD)
(20 cm²)² = (6 cm² * BD)²
400 cm^4 = 36 cm^4 * BD²
BD² = 400 cm^4 / 36 cm^4
BD² = 11.11 cm²

Taking the square root of both sides, we find:
BD = √11.11 cm
BD ≈ 3.33 cm

Therefore, the length of BD is approximately 3.33 cm.