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Question
A path 5 m wide runs along the inside of the rectangular field. The length of the rectangular field is three times the breadth of the field. If the area of the path is 500 m2 then find the length and breadth of the field
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Solution
Let the length of the rectangular field = ‘L’ m
Breadth of the rectangular field = ‘B’ m
Area of the rectangular field = (L × B) m2
Also given length = 3 × Breadth
L = 3B
Width of the path (W) = 5 m
Lenth of the inner rectangle = L – 2W
= l – 2(5)
= 3B – 10 m
Breadth of the inner rectangle = B – 2W
= B – 2(5)
= B – 10 m
Area of the inner rectangle = (3B – 10)(B – 10)
= 3B2 – 10B – 30B + 100
Area of the path = Area of outer rectangle – Area of inner rectangle
= (L × B) – (3B2 – 10B – 30B + 100)
= 3B × B – (3B2 – 40B + 100)
= 3B2 – 3B2 + 40B – 100
Area of the path = 40B – 100
Given area of the path = 500 m2
40B – 100 = 500
40B = 500 + 100 = 600
B = `600/40`
B = 15 m
Length of the field = 45 m, Breadth of the field = 15 m
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