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Question
Altitudes MN and MO of parallelogram MGHK are 8 cm and 4 cm long respectively (see figure). One side GH is 6 cm long. Find the perimeter of MGHK.
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Solution
Given, MGHK is a parallelogram, where MN = 8 cm, MO = 4 cm and GH = 6 cm
∴ Area of parallelogram MGHK, when base is GH ...[∵ Area of parallelogram = Base × Height]
= GH × MN
= 6 × 8 cm2
= 48 cm2 ...(i)
Area of paralielogram MGHK, when base is HK
= HK × MO
⇒ 48 = HK × 4 ...[From equation (i)]
⇒ HK = `48/4`
⇒ HK = 12 cm
In parallelogram, opposite sides are equal.
So, GH = MK = 6 cm and MG = HK = 12 cm
∴ Perimeter of parallelogram MGHK = (6 + 6 + 12 + 12) cm = 36 cm.
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