The perimeter of a parallelogram is 50, and the lengths of its heights are 2: 3. Find the length of the shorter side of the parallelogram.
1. Vertices of the parallelogram – A, B, C, D. BH and BK – heights drawn to AD and CD, respectively. P is the perimeter. S – area.
2. BН: BK = 2: 3
3. S = AD x BH, S = CD x BK.
AD x BH = CD x BK. Therefore, CD: AD = BH: BK = 2: 3.
AD = 3СD / 2.
4. Р = 2 (АD + СD) = 50 units of measurement.
AD + CD = 25 units. We substitute 3СD / 2 here instead of АD:
3СD / 2 + СD = 25 units of measurement.
CD = 10 units.
АD = 3СD / 2 = 15 units of measurement.
Answer: CD = 10 units of measure – the smaller side.
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