Question

is side of a square field measure 21m adjacent to the field there is a rectangular field having its sides in the ratio 4 ratio 3 if the perimeter of both the field are are equal find the dimensions of the rectangular field

Answer 1

Perimeter of a square = 4× Side

Perimeter of a rectangle = 2(length+Breadth)

Refer to the above attachment

Answer 2

Hey there!

I guess there are some grammatical errors in the question. So let me write the question properly again.

If the side of a square field measures 21m , Adjacent to the square field, there is a rectangular field having it's adjacent sides in the ratio of 4 : 3 . If the perimeter of both fields are equal. Find the dimensions of the field.

$\textbf{ Solution :}$

Given,
Side of the square field = 21m.

We know that,
Perimeter of the square = 4 * side

Now, Perimeter of square field = 4 * 21 = 84cm .

From the question,
Ratio of length and breadth = 4 : 3
Let the length be 4x , and breadth be 3x .

We know that,
Perimeter of the rectangle = 2 ( l + b)

So, Perimeter of the rectangular field = 2 ( 4x + 3x ) = 2(7x) = 14x .

According to the question,

Perimeter of square field = Perimeter of rectangular field.

84m = 14x

x = 84/14 = 42/7 = 6 .

Now,
Length of the rectangular field = 4x = 4 × 6 = 24m.
Breadth of the rectangular field = 3x = 3 × 6 = 18m .

Therefore the dimensions of the rectangular field are 24 * 18m .