Question

8. Each side of a square field measures 21 m. Adjacent to this field, there is a rectangular field
having its sides in the ratio 4 : 3. If the perimeters of both the fields are equal, find the
dimensions of the rectangular field.​

Answer 1

Answer:

48m and 36m

Step-by-step explanation:

Side of square field = 21m

Ratio of the sides of the field = 4 : 3

Perimeter of the square field = 21 × 4

= 84

Perimeter of rectangular field = (4+3=7) = 84 ÷ 7

= 12

12 × 4 = 48

12 × 3 = 36

Answer 2

Given:

• Measure of each side of a square field = 21m
• Ratio of the sides of the rectangular field = 4:3
• Perimeter of square field = Perimeter of rectangular field.

_________________________________

To find:

• Dimensions of the rectangular field.

_________________________________

Solution:

We are given the side of the square field, i.e. 21 m.

So,

Perimeter of square field = 4 × side

Perimeter = (4×21)m

$\boxed {\sf {\pink {Perimeter\ of\ square\ field = 84m}}}$

We are also given that,

Ratio of the sides of the rectangular field = 4:3

Perimeter of square field = Perimeter of rectangular field.

Let the length of the rectangle be 4x.

Let the breadth of the rectangle be 3x.

So,

Perimeter of rectangular field = 2(l+b)

84 = 2(4x+3x)

84 = 2×7x

84 = 14x

$\sf \dfrac {84}{14} = x$

$\boxed {\sf {\gray {6m = x}}}$

_________________________________

Dimensions of the rectangular field:

• Length = 4x

= 4×6

= 24m

• Breadth = 3x

= 3×6

= 18m

Hence, the dimensions of the rectangular field are 24m (length) and 18m (breadth).