Question

the area of a square field is 5184 ^.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

ATQ, the perimeter of the square field = perimeter of the rectangular field

given the area of the square field = 5184 units²

formula for the area of a square is side × side or side²

therefore side² = 5184 units²

➡ side = √5184

➡ side = 72 units

the side of the square field is 72 units

formula to find the perimeter of a square is 4 × side (since it has 4 equal sides)

perimeter of the square field = 4 × 72

= 288 units

➡ perimeter of the rectangular field is also 288 units.

now, it's given that the length of the rectangular field is twice it's breadth.

let the breadth of the rectangular field be x

therefore it's length 2x

perimeter of the rectangle = 2(l + b)

➡ 2(l + b) = 288 units

➡ 2x + x = 288/2

➡ 3x = 144

➡ x = 144/3

➡ x = 48 units

• breadth of the rectangular field = x = 48 units

• length of the rectangular field = 2x = 2 × 48 = 96 units

hence, it's area = l × b

= 48 × 96

= 4608 units²

Answer 2

$\mathsf{\huge{\underline{\boxed{Answer:- 460 unit^2}}}}$

$\rule{200}{2}$

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

Given :-

Area of square = 5184 unit²

Perimeter of square = Perimeter of rectangle

To find :-

Area of rectangle

Proof :-

Area if square = a²

a² = 5184 unit²

a = √5184

a = 72

So, side of square is 72 unit²

$\rule{200}{2}$

Perimeter of square = 4 × side

» 4 × 72 = perimeter

» 288 unit

So, Perimeter of rectangle is also 288units

$\rule{200}{2}$

let breadth of rectangle = x

So,

length = 2x

breadth = x

» 2(l + b) = 288 unit

» 2( x+2x) = 288 unit

» 2(3x) = 288 unit

» 6 x = 288 unit

» x = 288/6 unit

» x = 48 unit

__________________

Length = 2x

= 2(48)

= 96 unit

Breadth = x

= 48 unit

$\rule{200}{2}$

Area of rectangle = l × b

» 96 × 48 unit²

» 4608 unit ²

______________[Answer]________