The area of the parallelogram is 468 cm2, and its perimeter is 130 cm. Find the sides and heights
| August 12, 2021 | education
The area of the parallelogram is 468 cm2, and its perimeter is 130 cm. Find the sides and heights of the parallelogram if the difference in the lengths of the sides is 13cm.
Let’s use the picture to solve the problem.
Knowing that the perimeter is 130 cm, and the difference between the sides of the parallelogram is 13 cm, we find the sides.
P = 2 * AB + 2 * AD = 130.
AD – AB = 13.
130 = 2 * AB + 2 * (AB + 13) = 4 * AB + 26.
4 * AB = 104.
AB = 104/4 = 26 cm.
AD = 13 + 26 = 39 cm.
Sabcd = 468 cm2 = AD * BH = 39 * BH.
BH = 468/39 = 12 cm.
Answer: AB = 26 cm, AD = 38 cm, BH = 12 cm.
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