the side of parellogram are in the ratio 5 :4 and its area is 1000 cm square . Altitude on the greater side is 20 cm . The altitude on the smaller side is
Answers
Answer :-
Altitude on the smaller side is 25 cm [Option (b)]
Explanation :-
Ratio of the sides of the parallelogram = 5 : 4
Let the bigger side be 5x cm and smaller side be 4x cm
Area of Parallelogram = 1000 cm²
When bigger side is considered as base of the parallelogram
Base of the parallelogram (b) = 5x
Altitude on greater side i.e Height of the parallelogram (h) = 20 cm
Area of the parallelogram = bh
⇒ 1000 = 5x(20)
⇒ 1000/20 = 5x
⇒ 50 = 5x
⇒ 50/5 = x
⇒ 10 = x
⇒ x = 10
Smaller side = 4x = 4(10) = 40 cm
When smaller side is considered as the base of the parallelogram
Base of the the parallelogram (b) = 4x = 40 cm
Altitude on the smaller side i.e height of the parallelogram = h cm
Area of the parallelogram = bh
⇒ 1000 = 40(h)
⇒ 1000/40 = h
⇒ 100/4 = h
⇒ 25 = h
⇒ h = 25
∴ the altitude on the smaller side is 25 cm [Option (b)]