# 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.

RISHABH CHAURASIA
32 Points
8 years ago
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.
Aryan Bhagat
33 Points
8 years ago
Area of parallelogram is Base*height
So,we can take the area of parallelogram from two ways.
Base1 * Height1 =Base2 * Height2
27 * 12 = 36 * Height2
Height2=$\frac{27*12}{36}$
Height2 =9 units
Pooja
19 Points
7 years ago
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.
Pooja
19 Points
7 years ago
The area of a palallelogram and square are the same. If the perimeter of the square is 160.m . And the height of the parallelogramnis 20m sq. Find the length of the cotresponding basr of the parallelogram
Pooja
19 Points
7 years ago
The area of a parallelogram and a square are the same . If the perimeter of the square is 160m and the height of the parallelogram is 20m sq , find the length of the corrrsponding base of the parallelogram
Jagjeet Kaur
26 Points
7 years ago
Perimeter of a square=160mSide of a sq= perimeter÷4therefore side = 160/4=40mNow side of a square = 40mNow area of a sq = side square = 40×40 =1600m sqArea = 1600msqHeight of paralelogram = 20msqLength=?Now length= area/height =1600/20 =80m is length.ans
Sidhant
20 Points
6 years ago
The are of parrelogram and a square are same. If the perimeter of the square is 160m and the height parrelogram is 20m sq . Find length of the corresponding base of the parrelogram.