Question

The perimeter of a rectangular sheet is $ 110{\text{ cm}} $ . If the length is $ 30{\text{ cm}} $ , find its breadth also.

Answer 1

Hint: In order to find the breadth for the rectangle, whose perimeter is given, we must know what exactly the perimeter is. Perimeter is the sum of all the sides of a rectangle. Since there are two same lengths and two same breadths of a rectangle, the formula is described as: $ Perimeter = {\text{sum of all sides}} $ .
Formula used:
 $ Perimeter = 2\left( {length + breadth} \right) $

Complete step by step solution:
We are given the perimeter of the rectangular sheet that is $ 110{\text{ cm}} $ ,and also whose length is $ 30{\text{ cm}} $ .

We know that the perimeter is nothing but the sum of all the sides of the rectangle.
That numerically written as:
 $ Perimeter = length + breadth + length + breadth $
Since, we know that the opposite sides of a rectangle are the same, that means the length and the breadth are the same.
So, the perimeter becomes:
 $ Perimeter = 2length + 2breadth $
Taking $ 2 $ common from the above equation, we get:
 $ Perimeter = 2\left( {length + breadth} \right) $
Substituting the value of perimeter and breadth in the above equation, as given in the question, and we get:
 $ 110 = 2\left( {30 + breadth} \right) $
Dividing both the sides by $ 2 $ :
 $ \dfrac{{110}}{2} = \dfrac{{2\left( {30 + breadth} \right)}}{2} $
 $ \Rightarrow 55 = 30 + breadth $
Subtracting both the sides by $ 30 $ in the above equation and we get:
 $ \Rightarrow 55 - 30 = 30 + breadth - 30 $
 $ \Rightarrow 25 = breadth $
That can be written as $ breadth = 25{\text{ cm}} $ .
The rectangle now formed is:

Therefore, the breadth is $ 25{\text{ cm}} $ for the rectangular sheet whose perimeter is $ 110{\text{ cm}} $ and length is $ 30{\text{ cm}} $ .

Note: If we need to calculate the area of the rectangle, we can use the formula for area that is $Area = length \times breadth$.
A rectangle is a two-dimensional figure consisting of four sides, in which there are two lengths of equal size and two breadths of equal size and all the sides are perpendicular to each other.