The area of the parallelogram PQRS is 50 cm 2 . Find the distance between the parallel sides PQ and SR, if the length of the side PQ is 6 cm.
Let us draw a diagonal SQ of parallelogram PQRS and a perpendicular SX on the extended line PQ as shown in the figure.
here SX is drawn to find the distance between paralle side PQ and SR ... perpendicular SX is the distane between them.. .
We know that a diagonal of a parallelogram divides it into two congruent triangles. Also, congruent figures are equal in area.
∴ ar (ΔPQS) = ar (ΔQRS)
Area of parallelogram = ar (ΔPQS) + ar (ΔQRS) = 2 ar (ΔPQS)
∴ ar (ΔPQS) = 1/2 area of parallelogram=1/2*50cm2 = 25 cm2
Also, ar (ΔPQS) = 1/2 (PQ) (SX) = 25 cm2
⇒ (PQ) (SX) = 50 cm2
⇒ SX = 50cm/6(Since it is given that PQ = 6 cm)
⇒ SX = 8.34 cm
Thus, the distance between the parallel sides PQ and SR is 8.34 cm....