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

Answer:

side of square field is

(5184)^1/2...== 72m

perimeter = 4*72 = 288

coming to rectangle..

2 (2x+x) = 288

3x = 144

x = 48

other side = > 48*2 = 96

length = 96

breadth = 48

Answer 2

$\Large{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

Area of Rectangle = 4608 m²

$\large{\underline{\underline{\red{\mathfrak{Step-By-Step-Explanation:}}}}}$

$\tt given \begin{cases} \sf{Area \: of \: square \: field \: = \: 5184 \: m^2} \\ \sf{Length \: = \: 2 \: Breadth } \\ \sf{Perimeter \: of \: Square \: = \: Perimeter \: of \: Rectangle} \end{cases}$

We know Formula for Area of Square :

$\Large\leadsto {\underline{\boxed{\sf{Area \: = \: Side^2}}}}$

Put Values

⇒5184 = Side²

⇒Side = √5184

⇒Side = 72

∴ Side of Square = 72 m

__________________________________

Now use formula for Perimeter of square :

$\Large \leadsto {\underline{\boxed{\sf{Perimeter \: = \: 4 \: \times \: Side}}}}$

Put Values,

⇒Perimeter = 4*72

⇒Perimeter = 288 m

∴ Perimeter of square = 288 m

___________________________

Now, Come to Triangle

Take,

Breadth as b and length as 2b

As we know,

Perimeter of square = Perimeter of Rectangle

Use formula for Perimeter of rectangle

$\Large \leadsto {\underline{\boxed{\sf{Perimeter \: = \: 2(l \: + \: b)}}}}$

Put Values

⇒288 = 2(2b + b)

⇒288 = 2(3b)

⇒288 = 6b

⇒b = 288/6

⇒b = 48

Breadth = 48 m

Length = 48*2

⇒Length = 96

Length = 96 m

___________________________

Use formula for Area of rectangle :

$\Large \leadsto {\underline{\boxed{\sf{Area \: = \: lb}}}}$

Put Values

⇒Area = (48)(96)

⇒Area = 4608

$\LARGE \implies {\boxed{\boxed{\sf{Area \: = \: 4608 \: m^2}}}}$

___________________________

#answerwithquality

#BAL