The length and breadth of a rectangular park are in the ratio 5:2. A wide path Of 2m that runs all around the area of the park has an area 445sq.m. find the dimensions of park.
Answers
Answered by
0
Step-by-step explanation:
Given that area of the park be 305m^2.
Let the length of the park be 5x m and breadth be 2x m.
Therefore,
Area of the rectangular park = (5x) x (2x)
= 10x^2 m^2
Width of the path = 2.5 m
From the figure,
Outer length PQ = 5x m + 2.5 m + 2.5 m
= (5x + 5) m
Outer breadth QR = 2x + 2.5 m + 2.5 m
= (2x + 5) m
Area of PQRS = (5x + 5) m x (2x + 5) m
= (10x2 + 25x + 10x + 25) m^2
= (10x2 + 35x + 25) m^2
Area of the path = [(10x^2 + 35x + 25) – 10x^2] m^2
By solving above equation we get
305 = 35x + 25
305 – 25 = 35x
280 = 35x
x = 280/35 = 8
Therefore,
Length of the park = 5x
= 5 x 8 = 40 m
Similar questions