If the perimeter of a parallelogram is 140 m, the distance between a pair of opposite sides is 7 meters and its area is 210 sq m, find the length of two adjacent sides of the parallelogram.
The length is x and 70-x.
The area is 7x=210
Krish saturday september
To find the length of two adjacent sides of the parallelogram, we can use the given information about the perimeter, distance between opposite sides, and area of the parallelogram.
Let's start by considering the formula for the perimeter of a parallelogram:
Perimeter = 2 * (length of side 1 + length of side 2)
We are given that the perimeter is 140 m, so we can write the equation as:
140 = 2 * (length of side 1 + length of side 2) ---- (Equation 1)
Now, let's consider the formula for the area of a parallelogram:
Area = base * height
Since the distance between a pair of opposite sides is given as 7 meters, it represents the height of the parallelogram. We are given the area is 210 sq m, so we can write the equation as:
210 = base * 7 ---- (Equation 2)
To solve these two equations simultaneously, we need to eliminate one of the variables. Let's solve Equation 2 for the base:
base = 210 / 7 = 30 m
Now, substitute this value of base into Equation 1 and solve for the length of side 1 + length of side 2:
140 = 2 * (length of side 1 + length of side 2)
140 = 2 * (30 + length of side 2)
70 = 30 + length of side 2
length of side 2 = 70 - 30 = 40 m
Finally, we can calculate the length of side 1:
length of side 1 = 140 / 2 - length of side 2
length of side 1 = 70 - 40 = 30 m
Therefore, the length of two adjacent sides of the parallelogram is 30 meters.