Question

the area of a square is 1584m² a rectangular field whose length is twice its breadth has its perimeter equal to the perimeter of a square field find the area of rectangular field​

Answer 1

$\huge{\red{\underline{\underline{\sf{Given}}}}}$

The area of a square is 1584m²

A rectangular field whose length is twice its breadth has its perimeter equal to the perimeter of a square field

$\huge{\red{\underline{\underline{\sf{Find\:out}}}}}$

Find the area of rectangular field

$\huge{\red{\underline{\underline{\sf{Solution}}}}}$

Let the side of square field be a

Area of square = side × side

$\implies\sf 5184=a×a$

$\implies\sf a^2=5184$

$\implies\sf a=\sqrt{5184}=72m$ -----(i)

Perimeter of square field

$\implies\sf 4×side$

$\implies\sf 4×72$ -----using (i)

$\implies\sf 288m$ -----(ii)

According to the given condition

Again Let the breadth of rectangle be x then it's length be 2x

Perimeter of rectangle field = perimeter of square field

$\implies\sf 2(l+b)=4×side$

$\implies\sf 2(2x+x)=288$ -----using(ii)

$\implies\sf 2×3x=288$

$\implies\sf 6x=288$

$\implies\sf x=\cancel\frac{288}{6}$

$\implies\sf x=48m$

So,

$\large{\boxed{\bf{\red{Breadth=x=48m}}}}$

$\large{\boxed{\bf{\red{Length=2x=2×48=96}}}}$

Area of the rectangular field

= length × breadth

= 48 × 96

= 4608m²

$\large{\boxed{\bf{\red{Area\:of\:rectangular\:field=4608m^2}}}}$

Answer 2

$\bold{\huge{\fbox{\color{Black}{Given}}}}$

• Area of Square = 5184m^2

• Length of Rectangle (l) = Twice its breadth (2b)

• l = 2b ----(1)

• Perimeter of Square = Perimeter of Rectangle

$\bold{\huge{\fbox{\color{black}{Find}}}}$

• Area of Rectangular Field

$\bold{\huge{\fbox{\color{Black}{Solution}}}}$

• Area of Square = a^2

• $= > {a}^{2} = 5184 \\ = > a = \sqrt{5184} \\ = > a = 72m$

Hence,

• Side of Square (a) = 72m

• Perimeter of Square = 4a

• => 4 × 72 = 288m

Now,

A to Q:-

• Perimeter of Rectangle = Perimeter of Square

• => 2(l + b) = 288

• => (l + b) = 288/2 = 144

• => 2b + b = 144

• => 3b = 144

• => b = 144/3 = 48m

So,

• Lenth of Rectangle = l = 2b = 2×48 = 96m. ---(From - 1)

• Breadth of Rectangle = b = 48m

• Area of Rectangle = l × b = 96 × 48 = 4608m^2