The perimeter of a rectangle is $130\ cm$. If the breadth of the rectangle is $30\ cm$, find its length. Also find the area of the rectangle.

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Given: The perimeter of a rectangle is $130\ cm$. The breadth of the rectangle is $30\ cm$.

To do: To find the length and the area of the rectangle.

Solution: As given, the perimeter of the rectangle $P=130\ cm$

The breadth of the rectangle $b=30\ cm$

Let "$l$" be the length of the rectangle.

We know that, $P=2(l+b)$

$\Rightarrow 130\ cm=2(l+30\ cm)$

$\Rightarrow 130\ cm=2l+60\ cm$

$\Rightarrow 2l=130-60$

$\Rightarrow 2l=70$

$\Rightarrow l=\frac{70}{2}$

$\Rightarrow l=35\ cm$

So, the area of the rectangle $A=l\times b$

$=35\ cm\times 30\ cm$

$=1050\ cm^2$

Therefore, the length of the rectangle is $35\ cm$, and the area of the rectangle is $1050\ cm^2$.
Updated on 10-Oct-2022 13:35:52