9 grade maths> The adjacent sides of a parallelogram are...

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.

Kaavya Kalyan , 9 Years ago

Grade 9

7 Answers

RISHABH CHAURASIA

Last Activity: 9 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

Last Activity: 9 Years ago

Area of parallelogram is Base*height

So,we can take the area of parallelogram from two ways.

Base_{1 *}Height₁ =Base₂ * Height₂

27 * 12 = 36 * Height₂

Height₂= $\frac{27*12}{36}$

Height₂ =9 units

Pooja

Last Activity: 8 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

Last Activity: 8 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

Last Activity: 8 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

Last Activity: 8 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

Last Activity: 7 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.