ABCD-parallelogram; perimeter AOB = 21 cm; perimeter BОC = 24 cm; СD = 6 cm. Find the ABC perimeter.
August 29, 2021 | education|
Since ABCD is a parallelogram, AB = CD = 6 cm.
By condition, the perimeter of AOB = 21 cm, then BО + AO = 21 – AB = 21 – 6 = 15 cm.
The diagonals of the parallelogram at the intersection point are divided in half, then OA = OC.
Since AO + BО = 15 cm, and ОА = OC, then BО + OC = 15 cm.
Since, by condition, the perimeter of BOC = 24 cm, then BC = 24 – BO + OC = 24 – 15 = 9 cm.
Then the perimeter of the parallelogram is:
Ravsd = 2 * (AB + BC) = 2 * (6 + 9) = 30 cm.
Answer: Ravsd = 30 cm.
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