Question

The ratio of the length and breadth of a rectangular ground is 4:3 and its perimeter is 126 m.
(i) Find the length and breadth of the ground.
(ii) Find the area of the ground.​

Answer 1

Step-by-step explanation:

Let,

• The length of rectangular ground = 4x
• The breadth of rectangular ground = 3x

Perimeter of rectangular ground = 126 m

Perimeter of rectangle = 2 (length + breadth)

⇒ 2 (4x + 3x ) = 126

⇒ 8x + 6x = 126

⇒ 14x = 126

⇒ x = 126/14

⇒ x = 9

(i) The length and breadth of the ground :

★ Value of 4x :

⇒ 4 × 9

⇒ 36

The length of rectangular ground = 36 m

★ Value of 3x :

⇒ 3 × 9

⇒ 27

The breadth of rectangular ground = 27 m

(ii) The area of the ground :

Area of rectangle = length × breadth

⇒ 36 × 27

⇒ 972

Area of rectangular ground = 972 m²

Therefore,

(i) The length and breadth of rectangular ground is 36 m and 27 m respectively.

(ii) The area of the ground = 972 m².

Answer 2

Given :-

The ratio of the length and breadth of a rectangular ground is 4:3 and its perimeter is 126 m.

To Find :-

(i)  Find the length and breadth of the ground.

(ii) Find the area of the ground.​

Solution :-

Let

Length = 4y

Breadth = 3y

Ratio = 4y : 3y

Perimeter = 2(l + b)

126 = 2(l + b)

126/2 = l + b

63 = l + b

63 = 4y + 3y

63 = 7y

63/7 = y

9 = y

Now

Length = 4y = 4(9) = 36 m

Breadth = 3y = 3(9) = 27 m

Verification

Ratio = 36 : 27

Ratio = 4 : 3

Perimeter = 2(l + b)

126 = 2(36 + 27)

126 = 2(63)

126 = 126

Area = lb

Area = 36(27)

Area = 972 m²