Question

The perimeter of a rectangular park is 224 metres. Its breadth is three fourth of its length. What are the length and breadth of the park?

Answer 1

Step-by-step explanation:

Perimeter = 2(l+b)

b = 3/4 l

224 = 2(l+3/4l)

224 = 2(7/4l)

112 = 7/4l

l = 112×4/7

l = 448/7

l = 64

b = 3/4 × 64

b = 48

Answer 2

Required Answer :

Length of the park = 64 m

Breadth of the park = 48 m

Given :

• Perimeter of a rectangular park = 224 m
• The breadth of the park is three fourth of the length.

To find :

• Length and breadth of the park

Solution :

Let,

⇒ Length of the rectangular park = x metre

⇒ Breadth of the rectangular park = ¾ (length)

⇒ Breadth of the rectangular park = 3/4x metre

Now, by using the formula of the perimeter of rectangle we will find the value of x.

Formula of periemter of rectangle :

• Perimeter = 2(l + b)

where,

• l = length
• b = breadth

Substituting the given values :

⇒ 224 = 2(x + 3/4x)

⇒ 224/2 = x + 3/4x

⇒ 112 = x + 3/4x

⇒ 112 = (4x + 3x)/4

⇒ 112 = 7x/4

⇒ 112 × 4/7 = x

⇒ 16 × 4 = x

⇒ 64 = x

The value of x = 64

Substitute the value of 'x' in the length and breadth of the park :

LENGTH :

⇒ Length of the park = x

⇒ Length of the park = 64 m

BREADTH :

⇒ Breadth of the park = 3/4x

⇒ Breadth of the park = 3/4 × 64

⇒ Breadth of the park = 3/2 × 32

⇒ Breadth of the park = 3 × 16

⇒ Breadth of the park = 48 m