One of the diagonals of the parallelogram is its height is 9 cm find the side of the parallelogram if the area is 108 cm.

univerkov | January 8, 2021 | education

1. Vertices of the parallelogram – A, B, C, D. Diagonal ВD = 9 centimeters (perpendicular to the СD).
S – area.
2. We calculate the length of the side of the CD using the formula for calculating the area of a parallelogram:
S = СD x ВD = 108 centimeters².
СD = 108: 9 = 12 centimeters.
ВС = √ВD² + СD² (by the Pythagorean theorem).
BC = √81 + 144 = √225 = 15 centimeters.
Answer: sides of the parallelogram CD = AB = 12 centimeters, BC = AD = 15 centimeters.

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