Question

Question 86

Altitudes MN and MO of parallelogram MGHK are 8 cm and 4 cm long respectively in the below 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.
$\therefore$ Area of parallelogram MGHK, when base is GH $[\because$ area of parallelgram =base $\times$ height]
$=GH\times MN$
$=6\times 8c{m}^2=48c{m}^2$ ..............(i)
Area of parallelogram MGHK, when base is HK
$=HK\times MO$

$\Rightarrow 48=HK\times 4[fromEq.(i\left)\right]\Rightarrow HK=\frac{48}{4}\Rightarrow HK=12cm$
In parallelogram, opposite sides are equal.
So, GH = MK = 6 cm and MG = HK =12 cm
$\therefore$ Perimeter of parallelogram MGHK = (6 + 6 + 12 + 12) cm = 36 cm