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.

Answer 1

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.