The length of a rectangular lawn is two times of its breadth. If its perimeter is 120 m , find its length and breadth. The length and breadth of a rectangular park are in the ratio $$ 5: 2 $$. If its derimeter is 168 m , find its length and breadth.

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UpStudy AI · Accepted Answer

We can solve these problems by first expressing the relationships in equations and then using the formula for the perimeter of a rectangle.

Problem 1:
Given that the length (L) is two times the breadth (B), we have:
  L = 2B
The perimeter (P) of a rectangle is given by:
  P = 2(L + B)
Plug in the given perimeter (120 m) and the expression for L:
  2(2B + B) = 120
  2(3B) = 120
  6B = 120
Solve for B:
  B = 120 / 6 = 20 m
Now, find L:
  L = 2B = 2 × 20 = 40 m

Problem 2:
The length and breadth of a park are in the ratio 5:2. Let:
  L = 5k and B = 2k, where k is a constant.
The perimeter is given as 168 m:
  P = 2(L + B) = 2(5k + 2k) = 2(7k) = 14k
Set up the equation:
  14k = 168
Solve for k:
  k = 168 / 14 = 12
Now, find L and B:
  L = 5k = 5 × 12 = 60 m
  B = 2k = 2 × 12 = 24 m

Summary of Results:
- Rectangular Lawn: Length = 40 m and Breadth = 20 m.
- Rectangular Park: Length = 60 m and Breadth = 24 m.
Rectangular Lawn: Length = 40 m, Breadth = 20 m Rectangular Park: Length = 60 m, Breadth = 24 m

The length of a rectangular lawn is two times of its breadth. If its perimeter is 120 m , find its length and breadth. The length and breadth of a rectangular park are in the ratio \( 5: 2 \). If its derimeter is 168 m , find its length and breadth.

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