Question

The length of a rectangular field is 82cm. If its perimeter is 248cm, what is its breadth?

Answer 1

Hint: In this question, we are given the length and the perimeter of a rectangular field. We need to find the breadth of the rectangle. For this, we will use the formula of the perimeter of a rectangle. We will put values of perimeter and length and then find the value of breadth from the formed equation. The perimeter of a rectangular field with length l and breadth b is given as,
 $ \text{Perimeter}=2\left( l+b \right) $ .

Complete step by step answer:
Here we are given the length of the rectangular field as 82cm. So we can say that l = 82cm. Also, we are given that, the perimeter of the rectangular field is 248cm. So we can say that P = 248cm. Our rectangular field looks like this,

Let us suppose the breadth of the rectangular field as b.
Perimeter is the length of the boundary of the shape.
Therefore, perimeter of the rectangle is the sum of all sides. We know that the perimeter of the rectangular field of length l and breadth b is given as,
 $ \text{P}=2\left( l+b \right) $ .
Putting in the values of P and l, we get: $ \text{248}=2\left( 82+b \right) $ .
Solving it will give us the value of b.
Dividing both sides by 2 we get: $ 82+b=\dfrac{248}{2}\Rightarrow 82+b=124 $ .
Subtracting 82 from both sides we get: $ 82+b-82=124-82 $ .
Simplifying we get: $ b=42cm $ .
Hence the breadth of the rectangular field is 42cm.

Note:
Students should not forget to write units with found measurements. If they forget the formula of perimeter they should know that perimeter is the length of the boundary so, the perimeter will be equal to l+l+b+b (sum of all sides). Take care of the signs while solving the equation.