Question

the adjacent of aparallelogram are 36 cm and 27 cm im length.if the perpendicular distance between the shorter sides is 12cm find tje distence between the longer sides

Answer 1

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 longer sides is 9 cm