Question

Each side of a square field is 18m. Adjacent to this field here is a rectangular field having its sides in the ratio 5:4. If perimeters of both the fields are equal find the dimensions of the rectangular field​

Answer 1

Answer :

Length = 20 metres

Breadth = 16 metres

Step by step explanation :

It is given that :

Let the common multiple be x.

So, As the ratio is 5 : 4,

Let the Length of rectangular field be 5x and breadth be 4x

It's also given that :

Side of square field = 18 metres

Perimeter of rectangular field = Perimeter of square field.

So, As per your question,

2 [ Length + Breadth ] = 4 × side

2 [ 5x + 4x ] = 4 × 18

Simplifying it further :

2 × 9x = 72

18x = 72

Dividing both the sides, we get :

x = 4

Length = 5x = 5 × 4 = 20 metres

Breadth = 4x = 4 × 4 = 16 metres

Hence,

Length of the rectangular field is 20 metres and breadth is 16 metres.

Answer 2

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

The Length of the Rectangle is 20 m and Breadth is 16 m

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

Given :

Side of the square Field = 18 m

Ratio of the sides of the Rectangle = 5:4

To find :

The dimensions of the Rectangular field.

Solution :

As mentioned in the question, the Perimeter of the square = Perimeter of the Rectangle given.

So, first we need to find the Perimeter of the Square.

$\star$ Perimeter of Square =

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

$\sf{\implies18 \times 4}$

$\sf{\implies72}$

${\boxed{\bigstar{\sf\:{ Perimeter \: of \: Square = 72m}}}}$

According to the question,

Perimeter of the square = Perimeter of the Rectangle given.

Sides of the Rectangle = 5:4

Consider the Length if the Rectangle as 5x

Consider the Breadth of the Rectangle as 4x

$\star$ Perimeter of Rectangle =

$\sf{\implies2(5x + 4x) = 72}$

$\sf{\implies10x + 8x = 72}$

$\sf{\implies18x = 72}$

$\sf{\implies \: x = \dfrac{72}{18}}$

$\sf{\implies \: x = 4}$

Value of 5x

$\sf{\implies5 \times x}$

$\sf{\implies5 \times 4}$

$\sf{\implies20}$

${\boxed{\bigstar{\sf\:{Length \: of \: the \: rectangle = 20m}}}}$

Value of 4x

$\sf{\implies4 \times x}$

$\sf{\implies4 \times 4}$

$\sf{\implies16}$

${\boxed{\bigstar{\sf\:{Breadth\: of \: rectangle = 16m}}}}$

$\therefore$ The Length of the Rectangle is 20 m and Breadth is 16 m

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

$\star$ Perimeter of Rectangle =

$\sf{\implies2(20 + 16) = 72}$

$\sf{\implies40 + 32 = 72}$

$\sf{\implies72 = 72}$

Here, When we placed the value of x we got the required answer 72 m

$\therefore$ The Length of the Rectangle is 20 m and Breadth is 16 m