The lengths of the two sides of the parallelogram are proportional to the numbers 2 and 3.
| September 1, 2021 | education
The lengths of the two sides of the parallelogram are proportional to the numbers 2 and 3. Its perimeter is 280 cm. Find the lengths of all sides of the parallelogram.
1. Vertices of the parallelogram – A, B, C, D. The perimeter (P) of the parallelogram = 280 cm.
AB: AD = 2: 3.
2. АD = 3АВ / 2.
2.Considering that the sides of the parallelogram opposite each other (opposite) are equal, its perimeter is calculated by the formula:
P = 2 (AB + AD) = 280 cm.
AB + AD = 140 cm.
3. Substitute in this expression AD = 3AB / 2:
AB + 3AB / 2 = 140 cm.
5AB = 280 cm.
AB = 56 cm.
AD = 3AB / 2 = 84 cm.
Answer: AB = CD = 56 cm AD = BC = 84 cm.
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