Question

The perimeter of parallelogram ABCD is 42 cm. If AP = 3 cm and AQ = 4 cm, calculate the sides of parallelogram ABCD.

Answer 1

Let BC = x cm

We know that, 

Perimeter = 2(AB + BC)

⇒ 42 = 2(AB + x)

⇒ 21 = AB + x

⇒ AB = (21 – x) cm

Area of parallelogram = Base × Height

⇒ BC × AP = CD × AQ

⇒ x × 3 = 21 – x × 4

⇒ 3x = 84 – 4x

⇒ 7x = 84

⇒ x = `84/7` = 12

∴ BC = AD

= 12 cm

And AB = DC

= (21 – 12)

= 9 cm