Question

The area of square field is 5184m.square . A rectangular field whose length is twice it's breadth has its perimeter equal to the perimeter of the square field . Find the area of the rectangular Field. Answer step by step plz

Answer 1

Heya !!

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Given, area of square field = 5184 m²

So, area of square = a × a , where a is side of the square.

a² = 5184

=> a = √5184

=> a = 72 m

A.T.Q.
Length of the rectangle = 2x
and breadth of the rectangle = x

Given, Perimeter of square = Perimeter of rectangle

=> 4a = 2( l + b )

=> 4 × 72 = 2 ( 2x + x )

=> ( 4 × 72 ) / 2 = 2x + x

=> 2 × 72 = 3x

=> 144 = 3x

=> x = 144/3

=> x = 48

Thus, length of rectangle = 2x i.e., 2(48) = 96 m
and breadth of rectangle = x i.e., 48 m

Now, area of rectangle = l × b

=> 96 × 48

=> 4608 m²

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Answer 2

↑ Here is your answer ↓
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Area of a square field,

$s^2 = 5184$

$s = \sqrt{5184}$

$s = 72$

∴ Perimeter of this square,

$= 4s$

$=4*72$

$= 288$

Area of a rectangular field,

$= l*b$

Given that,

$b = x$

$l = 2x$

Sub it in the formula,

$= l*b$

$= 2x * x$

$= 2x^2 --(1)$

Now lets find the perimeter of rectangular field,

$= 2(l+b)$

$= 2(2x + x)$

$= 2(3x)$

$= 6x$

Equate it with perimeter of square,

$6x = 288$

$x = 288/6$

$x = 48$

Use (1) now to find the area,

$= 2x^2$

$= 2(48^2)$

$= 2*2304$

$= 4608 m^2$