Question

The perimeter of a parallelogram is 92 cm. If one side is greater than the adjacent side by 10 cm, find its length.

Answer 1

Hint: Assume that the length of parallelogram is ‘l’ and its breadth is ‘b’. Use the given information to determine the length of the parallelogram in terms of its breadth. Use the formula: perimeter of a parallelogram = 2(l + b) and equate this expression equal to 92 cm. Substitute the value of ‘l’ in terms of ‘b’ and form a linear equation in one variable ‘b’. Solve this equation to get the value of ‘b’ and hence find the value of ‘l’.

Complete step-by-step answer:
Let us assume that the length of the parallelogram is ‘l’ and its breadth is ‘b’.
We have been given that: the measure of one side is greater than the other side by 10 cm. Therefore mathematically,
l = b + 10………………..(i)

We know that the opposite sides of a parallelogram are equal, therefore, perimeter of a parallelogram is given by:
P = 2(l + b), where ‘P’ is the perimeter.
It is given that the perimeter of the parallelogram is 92 cm. Therefore,
P = 2(l + b) = 92
Substituting the value of ‘l’ from equation (i) in the above relation, we get,
2(b + 10 + b) = 92
2b + 10 = 46
2b = 36
b = 18 cm
Now, substituting the value of ‘b’ in equation (i), we get,
l = b + 10 = 18 + 10 = 28 cm
Hence, the length and breadth of the parallelogram are 28 cm and 18 cm respectively.

Note: One may note that here we have assumed length of the parallelogram greater than its breadth. It is not necessary to do so. You may assume its breadth is greater than the length. This will not alter our answer but only the numerical value of the measure of the sides will get interchanged. Do not use the relation of the area of the parallelogram because we have been provided with the information regarding its perimeter.