Question

The sides of a parallelogram are 24cm and 16cm. The distance between the 24cm sides is 8 cm. Find the distance between the 16cm sides

Answer 1

12 cm.

Explanation:

The distance between the opposite sides is a perpendicular line so we can form a right angled triangle by drawing a perpendicular line from one corner of the parallelogram to the opposite 24 cm side.

So one angle of the parallelogram will have a sine of 8/16 = 1/2 so this angle = 30 degrees.

In a similar way to the above we form a right angled triangle from the same corner by drawing a perpendicular line to the opposite 16 cm side.

This has an angle of 30 degrees ( opposite angles in a parallelogram are congruent).

So sine 30 = x / 24

1/2 = x /24

x = 12 feet.

Another way to do this is by noting that the 2 triangles are similar (because 2 corresponding angles are equal).

So 8/ 16 = x/24

16x = 192

x = 12 feet.