Question

The area of a square field is 5184 m2. A rectangular field, whose length is twice its
breadth, has its perimeter equal to the perimeter of the square field. Find the area

of the rectangular field.​

Answer 1

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Answer 2

$\textbf{\underline{\underline{Answer :-}}}$

The area of the Rectangle is 4608 m².

$\textbf{\underline{\underline{Explanation :-}}}$

$\textsf{\underline{\underline{Given :}}}$

The area of the Square = 5184 m²

Rectangular field whose ; length is twice its breadth.

$\textsf{\underline{\underline{To find :}}}$

The area of the rectangular field.

$\textsf{\underline{\underline{Solution :}}}$

First we need to find the measure of the side of the square.

Consider the measure of the side as x

★  $\textbf{As we know :}$

$\boxed{\sf{Area \: of \: Square = Side \times Side}}$

$\sf{\implies} \: x \times x = 5184$

$\sf{\implies} \:{x}^{2}= 5184$

$\sf{\implies} \: x =\sqrt{5184}$

$\sf{\implies} \: x = 72$

Side of the Square = 72 m

★  $\textbf{Perimeter of Square =}$

$\boxed{\sf{Perimeter = Side \times 4}}$

$\sf{\implies} \:72 \times 4$

$\sf{\implies} \:288$

Perimeter of the Square = 288 m

$\textbf{As Given in the Question,}$

Perimeter of Rectangle = Perimeter of Square.

The Length is twice the Breadth.

So,

Consider Breadth as x

Length as 2x

★  $\textbf{Perimeter of Rectangle =}$

$\boxed{\sf{Perimeter = 2(Length + Breadth)}}$

$\sf{\implies} \:288 = 2(x + 2x)$

$\sf{\implies} \:288 = 2x + 4x$

$\sf{\implies} \:288 = 6x$

$\sf{\implies} \:x =\dfrac{288}{6}$

$\sf{\implies} \:x = 48$

Breadth = 48

$\textbf{Value of 2x}$

$\sf{\implies} \:2 \times 48$

$\sf{\implies} \:96$

$\boxed{\sf{\red{Breadth = 48 \: m}}}$

$\boxed{\sf{\red{Length = 96 \: m}}}$

★ $\textbf{Area of Rectangle :}$

$\boxed{\sf{Area = Length \times Breadth}}$

$\sf{\implies} \:48 \times 96$

$\sf{\implies} \:4608$

$\therefore$ The area of the Rectangle is 4608 m².