Total area of quadrilateral ABCD is 20 cm 2 and offsets on BD are
2 cm and 3 cm. The length of BD is
The length of BD is 8 cm
To find the length of BD, we need to use the concept of offsets in a quadrilateral.
First, let's understand what the offsets are. In a quadrilateral, offsets are the distances between the opposite sides measured along the perpendiculars drawn from one side to the opposite side. In this case, the offsets on BD are given as 2 cm and 3 cm.
Now, let's denote the lengths of the offsets as x and y, where x = 2 cm and y = 3 cm.
To find the length of BD, we need to use the formula for the area of a quadrilateral. The area of a quadrilateral can be calculated using the formula:
Area = 1/2 * (Product of diagonals) * (Sum of offsets)
In this case, the area of ABCD is given as 20 cm^2, so we have:
20 = 1/2 * (BD) * (x + y)
Substituting the values of x and y, we get:
20 = 1/2 * (BD) * (2 + 3)
20 = 5/2 * (BD)
Multiplying both sides by 2/5, we can isolate BD:
(2/5) * 20 = BD
Simplifying, we have:
8 = BD
Therefore, the length of BD is 8 cm.