Question

urgent!! - What is the perimeter of a parallelogram, if it's area is 36 cm2 and the distances between the point of intersection of the diagonals and the sides are 2 cm and 3 cm?

Answer 1

30 cm

Explanation:

The distance from the intersection of the diagonals (center of the parallelogram) to one side is half the height when that side is considered the base.

So, if the height is 2×(2 cm) = 4 cm, and the area is 36 cm², the base for that height must be ...

(36 cm²)/(4 cm) = 9 cm.

Similarly, if the height is 2×(3 cm) = 6 cm, the base for that height is ...

(36 cm²)/(6 cm) = 6 cm.

These "bases" are the side lengths of the parallelogram, so its perimeter is ...

P = 2(s1 +s2) = 2(9 cm +6 cm) = 30 cm

The perimeter of the parallelogram is 30 cm.