Question

In the given figure, the perimeter of parallelogram PQRS is 42 cm. Find the lengths of PQ and PS.

Answer 1

Area of ||gm PQRS = PQ x 6
Also, 
Area of ||gm PQRS = PS x 8
∴ PQ x 6 = PS x 8

⇒ PQ = ${\displaystyle \frac{8\text{PS}}{6}}$

⇒ PQ = ${\displaystyle \frac{4\text{PS}}{3}}$  ....(i)

Perimeter of ||gm PQRS = PQ + OR + RS + PS
⇒ 42 = 2PQ + 2PS  ...(opposite sides of a parallelogram are equal)
⇒ 21 = PQ + PS

⇒ ${\displaystyle \frac{4\text{PS}}{3}+\text{PS}}$ = 21   ...[From (i)]

⇒ ${\displaystyle \frac{4\text{PS}+3\text{PS}}{3}}$

⇒ 7PS = 63
⇒ PS = 9cm
Now,

PQ = ${\displaystyle \frac{4\text{PS}}{3}}$

= ${\displaystyle \frac{4\times 9}{3}}$
= 12cm
∴ PQ = 12cm and PS = 9cm.