Question

the area of square field is 576 meter square .a rectangular field whose length is twice by its breadth . it's perimeter equal to the perimeter of square field . find the rectangular field​

Answer 1

Step-by-step explanation:

area of square=a²

√576. =a

24. =a

suppose length of rectangle is 2x

breadth of rectangle is x

perimeter of square = perimeter of rectangle

4×side. = 2(length+breadth)

4×24. = 2(2x+x)

96. = 4x+2x

96. = 6x

96. = x

6

16=x

length of rectangle=2×16=32

breadth of rectangle=1×16=16

I hope I have helped u.

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Length of the Rectangle is 32 m and Breadth is 16 m.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Area of the Rectangle = 576 m².

Length of the Rectangle = Twice it's Breadth

Perimeter of the Rectangle = Perimeter of Square

To Find :

The dimensions of Rectangular Field.

Solution :

First We need to find the Measure of the side of the Square.

We are given with the area, so the side can be found.

$\rule{300}{1.5}$

Consider the side of Square as x

★ $\boxed{\sf{Area = Side \times Side}}$

$\sf{\implies} \: x \times x = 576$

$\sf{\implies} \: {x}^{2} = 576$

$\sf{\implies} \: x = \sqrt{576}$

$\sf{\implies} \: x = 24$

The side of the Square is 24 m

$\rule{300}{1.5}$

As We got the Measure of the side, we can now find the Perimeter of the Square

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

$\sf{\implies} \: 24 \times 4$

$\sf{\implies} \: 96$

The Perimeter of Square is 96 m

$\rule{300}{1.5}$

According to the Question,

Perimeter of Square = Perimeter of the Rectangle

Consider the Breadth as x

Length as 2x

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

$\sf{\implies} \: 2(2x + x) = 96$

$\sf{\implies} \: 4x + 2x = 96$

$\sf{\implies} \: 6x = 96$

$\sf{\implies} \: x = \dfrac{96}{6}$

$\sf{\implies} \: x = 16$

★ Value of 2x

$\sf{\implies} \: 16 \times 2$

$\sf{\implies} \: 32$

$\therefore$ The Length of the Rectangle is 32 m and Breadth is 16 m.