Question

the length and breadth of a rectangular park are in the ratio of 5:2. a wide path of 2.5m that runs all around the park has an area of 445 sq m . Find the dimension of the park

Answer 1

Answer is in the pic below
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Answer 2

Length of park is 60 m and breadth of park is 24 m.

Step-by-step explanation:

1. Area of path = 445 $(m^{2})$.

2. Ratio of length to breadth =$\frac{l}{b}=\frac{5}{2}=\frac{5x}{2x}$

  Means

  length of park =$5x$

 breadth of park =$2x$

 So area of park$(A_{i})$ = $l\times b=5x\times 2x=10x^{2}$     ...1)

3. Length of park including path on both side(L) = $5x+2\times 2.5$=$5x+5$

   Breadth of park including path on both side(B) = $2x+2\times 2.5$=$2x+5$

  So Area of park including path $(A_{o})=L\times B=(5x+5)\times (2x+5)=10x^{2}+35x+25$      ...2)

4. So

  Area of park including path - area of park =Area of path

  $A_{o}-A_{i}$ = 445    ...3)

5. From equation 1,2 and equation 3)

   $10x^{2}+35x+25-10x^{2}=445$

    $35x+25=445$

   So on solving

   $x$ =12

6. Length of park =$5x$ =5×12=60 m

    Breadth of park =$2x$=2×12=24 m