Question

The adjacent sides of a parallelogram are 30cm and 24cm in length. if the perpendicular distance between the shorter sides is 12cm, what is the distance between the longer sides?

Answer 1

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The adjacent sides of a parallelogram are 36cm and 27cm in length .If the distance between the shorter sides is 12cm, find the distance between the longer sides.

2 years ago

Answers : (6)

Let the parallelogram be ABCD with AB=CD=36 cm and AD=CB=27 cm. Let DE be the altitude from D on BC and AF be the altitude from A on CD. The shortest distance between the shorter sides is 12 cm.

 

We know that the perpendicular distance is the shortest distance between two points. So we can say that altitude DE is the shortest distance between the two short sides AD & BC. Therefore, DE=12 cm.

 

Now, we know that Area of Parallelogram = ½ X Base X Height. 

So Area of Parallelogram ABCD = ½ X AD X DE = ½ X AF X DC

     Area of Parallelogram ABCD = ½ X 27 X 12 = ½ X AF X 36

     Area of Parallelogram ABCD = ½ X 324 = ½ X AF X 36       

                                               =  324 =  AF X 36   

                                               =  AF   = 324/36 

                                               =  AF   =  9 cm         

Therefore the shortest distance between the two loger sides is 9 cm.  

Answer 2

the distance between longer sides is 9.6 cm