Question

The area of a square field is 4096 Sq.m. A rectangular field, whose length is thrice its breadth, has its perimeter equal to the perimeter of square field.
Q. The breadth of the rectangular field
(A)64m
(B)32m
(C)96m
(D)16m
​

Answer 1

Answer:

The breadth of the rectangular field is 96m [0ptionC].

Step-by-step explanation:

Given, the area of a square field is 4096m².

Let the side of the square field be x meters.

We know that :

➻ Area of a square = s²

➻ 4096m² = x²

➻ √4096m² = x

➻ 64m = x

∴ The length of the side of the square is 64m.

Now, let's find the perimeter of the square :

➻ Perimeter of a square = 4s

➻ P = 4 × 64m

➻ P = 256m

∴ The perimeter of the square is 256m.

Given that, a rectangular field is having the same perimeter as of the square perimeter.

➻ P of rectangle = P of square

Let, according to the question :

➻ Breadth be b meters

➻ Length be 3b meters

Let's now find the value of 'b' :

➻ Perimeter of rectangle = 2 (l + b)

➻ 256m = 2 (3b + b)

➻ 256m = 2 × 4b

➻ 256m = 8b

➻ 256m/8 = b

➻ 32m = b

Substituting the value of 'b' values :

➻ Breadth = b : 32m

➻ Length = 3b : 96m

∴ The length and breadth of the rectangular field are 96m and 32m respectively.