# The perimeter of a parallelogram is 150 cm and one of its sides is greater than the other by 25 cm. Find the lengths of all the sides of that parallelogram.

Last updated date: 21st Mar 2023

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Answer

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Hint- Here, we will proceed by using the formula for the perimeter of the parallelogram.

Let the length and breadth of the parallelogram be $l$ and $b$

Given, the length of the parallelogram is greater than the breadth of the parallelogram by 25 cm

i.e., $l - b = 25{\text{ }} \to {\text{(1)}}$

Also, given the perimeter of the parallelogram is $P = 150$ cm

As we know that the perimeter of the parallelogram is given by $P = 2l + 2b$

$

\Rightarrow 150 = 2l + 2b \Rightarrow 2\left( {l + b} \right) = 150 \\

\Rightarrow l + b = 75{\text{ }} \to {\text{(2)}} \\

$

Now adding equations (1) and (2), we get

$ \Rightarrow l - b + l + b = 25 + 75 \Rightarrow 2l = 100 \Rightarrow l = 50{\text{ cm}}$

Put $l = 50$ in equation (1), we have

$50 - b = 25 \Rightarrow b = 50 - 25 = 25{\text{ cm}}$

Therefore, the length of the parallelogram is 50 cm and the breadth of the parallelogram is 25 cm.

Note- Perimeter is calculated simply by measuring the boundary of any figure. Here, in case of parallelogram it will be the sum of all the four sides consisting of two times the length of the parallelogram and two times the breadth of the parallelogram.

Let the length and breadth of the parallelogram be $l$ and $b$

Given, the length of the parallelogram is greater than the breadth of the parallelogram by 25 cm

i.e., $l - b = 25{\text{ }} \to {\text{(1)}}$

Also, given the perimeter of the parallelogram is $P = 150$ cm

As we know that the perimeter of the parallelogram is given by $P = 2l + 2b$

$

\Rightarrow 150 = 2l + 2b \Rightarrow 2\left( {l + b} \right) = 150 \\

\Rightarrow l + b = 75{\text{ }} \to {\text{(2)}} \\

$

Now adding equations (1) and (2), we get

$ \Rightarrow l - b + l + b = 25 + 75 \Rightarrow 2l = 100 \Rightarrow l = 50{\text{ cm}}$

Put $l = 50$ in equation (1), we have

$50 - b = 25 \Rightarrow b = 50 - 25 = 25{\text{ cm}}$

Therefore, the length of the parallelogram is 50 cm and the breadth of the parallelogram is 25 cm.

Note- Perimeter is calculated simply by measuring the boundary of any figure. Here, in case of parallelogram it will be the sum of all the four sides consisting of two times the length of the parallelogram and two times the breadth of the parallelogram.

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