Question

A garden $ 50m $ long and $ 35m $ broad is to be fenced with wire. How much long wire is required to fence the whole garden?

Answer 1

Hint: In the given question, we are provided with the dimensions of a rectangular garden that is to be fenced with wire. The perimeter of a rectangle is the sum of the lengths of its boundaries. So, we substitute the values of length and breadth in the formula for the perimeter of a rectangle. Perimeter of a rectangle is $ 2\left( {l + b} \right) $ , where l and b are the length and breadth of the rectangle respectively. We also must have knowledge of simplification rules and BODMAS in order to simplify the calculations and get to the final answer.

Complete step-by-step answer:
According to the question,
The length of the garden $ = l = 50m $
The breadth of the garden $ = b = 35m $
Now, we have to calculate the length of the wire that will be required in order to fence the whole rectangular garden. So, we will have to calculate the perimeter of the rectangular garden.
Now, we also know that the perimeter of a rectangle is calculated using the formula $ 2\left( {l + b} \right) $ , where l and b are the length and breadth of the rectangle respectively.
So, Perimeter of garden $ = 2\left( {l + b} \right) $
 $ = 2\left( {50m + 35m} \right) $
Adding up the terms and simplifying the expression, we get,
 $ = 2\left( {85m} \right) $
 $ = 170m $
Hence, the perimeter of a rectangular garden is $ 170m $ .
So, the length of the wire required to fence the garden is $ 170m $ .
So, the correct answer is “ $ 170\;m $ ”.

Note: We must ensure that both the length and breadth of a rectangle are expressed in the same units of measurement. One must know the formulae for calculating the perimeter and area of some basic geometric shapes in order to work out these types of problems. We must practice many problems on mensuration so that we get familiar with the problems and know when to use the formula for perimeter and area.