Question

The area of a parallelogram is $780$ sq. cm. If the length of one side is $26$cm, find the length of the other side.

Answer 1

Hint:
We know that in parallelogram the parallel sides are equal in length so assume the length of the other side to be b cm. Then use the formula of area of the parallelogram which is given as-
Area of Parallelogram= Base × Height
Put the given values in this formula and solve for b to get the answer.

Complete step by step solution:
Given, the area of a parallelogram =$780$ sq. cm
Length of one side=$26$cm
We have to find the length of the other side.
Now, let the parallelogram be ABCD, where AB=CD=$26$cm because we know that the parallel sides in a parallelogram are equal in length
Assume the length of side AD is b cm.

Now we know that the formula of area of the parallelogram is given by-
Area of Parallelogram= Base × Height
On putting the given values, we get-
Area of parallelogram=$26 \times b$
We also know the value of the area of the parallelogram, so putting the value we get-
$ \Rightarrow 780 = 26 \times b$
On adjusting, we get-
$ \Rightarrow b = \dfrac{{780}}{{26}}$
On simplifying, we get-
$ \Rightarrow b = \dfrac{{390}}{{13}}$
On division, we get-
$ \Rightarrow $ b=$30$ cm.

Hence the length of the other side is $30$ cm.

Note:
The properties of the parallelogram are-
1) The opposite sides and opposite angles of the parallelogram are equal.
2) The consecutive angles of the parallelogram are supplementary angles which means their sum is equal to ${180^\circ }$.
3) If one angle of the parallelogram is a right angle then all the other angles will also be the right angle.
4) The diagonals of the parallelogram bisect each other and form two congruent triangles.