question_answer

The area of a rectangular field whose length is twice its breadth is 2450 m2. Find the perimeter of the field.

Answer:

Let the breadth of the field be x metres. Then, length of the field be 2x metres.

Therefore, area of the rectangular field

= length \[\times \]breadth

\[=\text{ }\left( 2x \right)\left( x \right)=\left( 2{{x}^{2}} \right)\text{ }{{m}^{2}}\]

Given that area is 2450\[{{m}^{2}}\].

Therefore, \[2{{x}^{2}}=2450\]

\[{{x}^{2}}=\frac{2450}{2}\]

\[x=\sqrt{1225}\]

or x = 35 m

Hence, breadth = 35 m and length \[35\text{ }\times \text{ }2\]

= 70 m

Perimeter to the field \[=2\left( l+b \right)\]

\[=2\left( 70+35 \right)\text{ }m\]

\[=2\times 105\text{ }m\]

= 210 m