the length and breadth of a rectangular Park are in the ratio 5 is to 2. a 2.5 M wide path running all around the outside the park has an area 305 m square. find the dimensions of the park
Answers
The dimensions of the rectangular park are 40 m x 16 m.
Step-by-step explanation:
The ratio of the length and breadth of the rectangular park = 5:2
So, let the length of the park be “5x” and the breadth of the park be “2x”.
∴ The area of the rectangular park = length × breadth = 5x × 2x = 10x² ….. (i)
It is given that a path of 2.5 m wide runs all around outside the park, therefore,
New Length = 5x + (2*2.5) = [5x + 5]
New Breadth = 2x + (2*2.5) = [2x + 5]
∴ The area of the rectangular park along with the path around it = length * breadth = [5x + 5] × [2x + 5] ……. (ii)
The area of the path is given as 305 sq. meter. …… (iii)
Therefore, we get
Area of the path = [Area of the rectangular park along with the path around it] – [Area of the rectangular park]
substituting from (i), (ii) & (iii)
305 = [(5x+5)(2x+5)] - 10x²
⇒ 305 = 10x² + 25x + 10x + 25 – 10x²
⇒ 305 = 35x + 25
⇒ 35 x = 280
⇒ x = 280/35
⇒ x = 8 m
Thus, the dimensions of the rectangular park is given as,
Length = 5x = 5*8 = 40 m
and
Breadth = 2x = 2*8 = 16 m
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