Question

the length and the breadth of a rectangular field are in the ratio 4:3 and its perimeter is 112m its area is

Answer 1

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Answer 2

$\textbf{\underline{\underline{Answer :-}}}$

The area of the Rectangle is 768 m² .

$\textbf{\underline{\underline{Explanation :-}}}$

Given :

The ratio = 4 : 3

Perimeter of Rectangle = 112 m

To find :

The area of the Rectangle

Solution :

Consider the Length as 4x

Consider the Breadth as 3x

$\star$ Perimeter of Rectangle =

$\sf{\implies2(length + breadth)}$

$\sf{\implies2(4x + 3x) = 112}$

$\sf{\implies8x + 6x= 112}$

$\sf{\implies14x = 112}$

$\sf{\implies}x = \dfrac{112}{14}$

$\sf{\implies}x = 8$

${\boxed{\bigstar{\sf\:{x = 8}}}}$

Value of 4x

$\sf{\implies}4 \times x$

$\sf{\implies}4 \times 8$

$\sf{\implies}32$

${\boxed{\bigstar{\sf\:{length = 32 \:m}}}}$

Value of 3x

$\sf{\implies}3 \times x$

$\sf{\implies}3 \times 8$

$\sf{\implies}24$

${\boxed{\bigstar{\sf\:{breadth= 24 \:m}}}}$

Length = 32 m

Breadth = 24 m

$\star$ Area of Rectangle

$\sf{\implies}length \times breadth$

$\sf{\implies}32 \times 24$

$\sf{\implies}768$

${\boxed{\bigstar{\sf\:{area \: of \: the \: rectangle = 768 {m}^{2}}}}}$

$\therefore$ The area of the Rectangle is 768 m² .