Question

The length of a rectangular plot is twice its breadth.If the perimeter of the plot be

1200m,find its area
​

Answer 1

Given: The length of a rectangular plot is twice its breadth, and the perimeter of the plot be 1200m.

⠀

Exigency to find: The area of a rectangle plot.

⠀

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀

❒ Let us consider that, the breadth of rectangular plot be x m.

⠀

Given that,

• The length of a rectangular plot is twice its breadth.

⠀

Therefore,

⠀

$\sf{ \leadsto \: \: Length = \textsf{\textbf{2x m.}}}$

⠀

We know that, if we are given with the perimeter of rectangle, length of rectangle & breadth of rectangle, we have the required formula, that is,

⠀

$\sf{:\implies Perimeter_{(rectangle)} = 2(l + b)}$

⠀

⠀⠀⠀⠀ Here l is the length of rectangle in meter and b is the breadth of rectangle in meters. And here we have given the values of perimeter of rectangle, perimeter of rectangle is 1200m, l = 2x & b = x. So, by using the required formula we can calculate the value of 'x'.

⠀

By using the required formula, and substituting all the given values in the formula, we get:

⠀

$\sf{:\implies 1200 = 2(2x + x)} \\ \\ \\ \sf{:\implies 1200 = 2(3x)} \\ \\ \\ \sf{:\implies 1200 = 6x} \\ \\ \\ \sf{:\implies x = \dfrac{1200}{6}} \\ \\ \\ \sf{:\implies \boxed{ \frak{ \purple{x = 200}}}}$

⠀

Therefore,

⠀

• Length, 2x = 2 × 200 = 400m.
• Breadth, x = 200m.

⠀

Now,

⠀

We know that, if we are given with the length of rectangle & breadth of rectangle, we have the required formula, that is,

⠀

$\sf{:\implies Area_{(rectangle)} = l \times b}$

⠀

⠀⠀⠀⠀ Here l is the length of rectangle in meter and b is the breadth of rectangle in meters. And here here we have given the values of length and breadth of rectangle respectively, l = 400m & b = 200m. So, by using using the required formula we can find the area of rectangle.

⠀

By using the required formula, and substituting all the given values in the formula, we get:

⠀

$\sf{:\implies Area_{(rectangle)} = 400 \times 200} \\ \\ \\ \sf{:\implies \boxed{ \frak{ \pink{Area_{(rectangle)} = 80000}}}}$

⠀

$\sf{\therefore \underline{The \; area \; of \; rectangle \; is \; \textsf{\textbf{80000{m}}}^{ \textsf{\textbf{2}}}.}}$

Answer 2

Question:-

• The length of a rectangular plot is twice its breadth.If the perimeter of the plot be 1200m , find its area.

Given:-

• The length of rectangle plot is twice its breadth.

Solution:-

• Let the breadth be " x "

• Length is twice its breadth then length is " 2x "

$\tt\implies \: Perimeter = 2( l + b )$

$\tt\implies \: 1200 = 2( 2x + x )$

$\tt\implies \: 1200 = 2( 3x )$

$\tt\implies \: 1200 = 6x$

$\tt\implies \: x = \cancel\dfrac { 1200 } { 6 }$

$\tt\implies \: x = 200$

Hence ,

• Length is 2x = 400 m

• Breadth is 200 m

Now ,

We have to find the Area:-

$\tt\implies \: Area of rectangle = length \times breadth$

$\tt\implies \: 400 \times 200$

$\tt\implies \: 80000$

Hence ,

• Area is $\tt { 80000 m }^{ 2 }$