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?
Answers
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
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