The parallel sides of a trapezium are in ratio 3:4 and perpendicular distance between them is 16cm. If the area of trapezium is 720cm², find the lengths of parallel sides.
Answers
Correct question :
The parallel sides of a trapezium are in ratio 2 : 3 and perpendicular distance between them is 16cm. If the area of trapezium is 720cm², find the lengths of parallel sides.
Given :
The parallel sides of a trapezium are in ratio 2 : 3 and perpendicular distance between them is 16cm. The area of trapezium is 720cm².
To find :
Find the lengths of parallel sides.
Solution :
Let the parallel sides of trapezium be '2x' and '3x' respectively.
Perpendicular distance between them, height = 16 cm
Area of trapezium = 720 cm²
∵ Area of trapezium = 1/2 × (Sum of parallel sides) × Height
Now according to question :
⇒ 720 = 1/2 × (2x + 3x) × 16
⇒ 720 = 8 × 5x
⇒ 720/8 = 5x
⇒ 90 = 5x
⇒ x = 90/5
⇒ x = 18
∴ Parallel sides of trapezium :
Length of one parallel side = 2x = 2 × 18 = 36 cm.
Length of other parallel side = 3x = 3 × 18 = 54 cm
Therefore,