The parallelogram heights are 8cm and 6cm, and its area is 72cm squared. Find the perimeter of the parallelogram.

| April 18, 2021 | education

Let us denote by x the length of the side of this parallelogram, to which the height of 8 cm is lowered, and through y, the length of the side of this parallelogram, to which the height of 6 cm is lowered.

According to the condition of the problem, the area of ​​this parallelogram is 72 cm².

Since the area of ​​a parallelogram is equal to the product of the height of this parallelogram and the length of the side to which the height is lowered, we can compose the following equations:

x * 8 = 72

and

y * 6 = 72.

From the first equation we find x:

x = 72/8 = 9 cm.

From the second equation we find y:

y = 72/6 = 12 cm.

Knowing the lengths of the sides of this parallelogram, we find its perimeter:

2 * (9 + 12) = 2 * 21 = 42 cm.

Answer: the perimeter of this parallelogram is 42 cm.



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