Question

The area of the rectangular field is 3400\[{m^2}\]and its length is 68m. Find the distance covered by a man going 5 times around the field.

Answer 1

Hint: We calculate the breadth of the rectangular field by substituting values in formula of area. Use the formula of perimeter to calculate distance covered in one round. Use a unitary method to calculate distance covered in 5 rounds.
* A rectangle is a quadrilateral having four sides, where opposite sides are equal and parallel. If length of rectangle is ‘l’ and breadth of rectangle is ‘b’ then area of rectangle is \[l \times b\]
* Perimeter of rectangle is \[2(l + b)\]
* Unitary method helps us to calculate the value of multiple units by multiplying the value of a single unit to the number of units given.

Complete step by step answer:
We are given that the length of the rectangular field is 68m.
\[ \Rightarrow l = 68\] … (1)
Assume breadth of the field as ‘b’.
Let us denote area by A
Since we are given the area of rectangular field is 3400\[{m^2}\]
\[ \Rightarrow A = 3400\]
We know area is given from the formula \[l \times b\]
\[ \Rightarrow l \times b = 3400\]
Substitute value of length from equation (1)
\[ \Rightarrow 68 \times b = 3400\]
Cancel same factors from both sides of the equation
\[ \Rightarrow b = 50\] … (2)
Now we calculate perimeter of rectangular field.
\[ \Rightarrow \]Perimeter of field\[ = 2(l + b)\]
\[ \Rightarrow \]Perimeter of field\[ = 2(68 + 50)\]
\[ \Rightarrow \]Perimeter of field\[ = 2 \times 118\]
\[ \Rightarrow \]Perimeter of field\[ = 236\]m
So, distance covered by man in 1 round \[ = 236\]m
Use a unitary method to calculate the value of multiple units.
\[ \Rightarrow \] Distance covered by man in 5 rounds \[ = 236 \times 5\]m
\[ \Rightarrow \] Distance covered by man in 5 rounds \[ = 1180\]m

\[\therefore \] Distance covered by man in 5 rounds is 1180m.

Note: Many students make mistakes in calculation of breadth as they tend to leave huge numbers in fraction form, keep in mind we calculate if they cancel out if not we write the value of breadth in decimal form.