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.
Since you have the height = 7, the area is base * height = 210 = 7b
so, b=30, one of the two sides.
The perimiter = 2a+2b = 2a + 60 = 140, so a = 40
The sides are 30 and 40
Math
To find the length of two adjacent sides of the parallelogram, follow these steps:
Step 1: Understand the problem.
A parallelogram is a four-sided polygon with opposite sides that are parallel and equal in length. Given the information, we need to find the length of two adjacent sides.
Step 2: Use the formulas.
The perimeter of a parallelogram is given by the formula:
Perimeter = 2(a + b)
where a and b are the lengths of two adjacent sides.
Step 3: Find the perimeter.
From the given information, we know the perimeter is 140 m. Therefore, we can write the equation as:
140 = 2(a + b)
Step 4: Solve the equation.
Divide both sides of the equation by 2 to isolate (a + b):
70 = a + b
Step 5: Use the formula for the area.
The area of a parallelogram is given by the formula:
Area = base × height
Given that the distance between a pair of opposite sides is 7 meters, we can use this formula to find the area:
210 = 7 × base
Step 6: Solve for the base.
Divide both sides of the equation by 7:
base = 210 / 7
base = 30 meters
Step 7: Use the area and base to find the height.
Since the height of the parallelogram is the distance between a pair of opposite sides, the height is 7 meters.
Step 8: Find the lengths of the adjacent sides using the area and height.
Since the area of a parallelogram is given by the formula Area = base × height, we can rearrange the formula to find the lengths of the adjacent sides:
Area = base × height
210 = a × 7
30 = a
Step 9: The lengths of the adjacent sides are 30 meters.
So, the lengths of the adjacent sides of the parallelogram are both 30 meters.