A path 5 m wide runs along inside a rectangular field . The length of the rectangular field is 3 times the breadth of the field. if the area of the path is 500 m² , them find the length and breadth of the field.
Lenght = 45, Breadth = 15
Answers
ANsWeR :-
Let the length of the rectangular field = ‘L’ m
Breadth of the rectangular field = ‘B’ m
Area of the rectangular field = (L x B) m²
Also given :-
length = 3 x Breadth
Width of the path (W) = 5m
Length of the inner rectangle = L – 2W = l – 2(5) = 3B – 10m
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 x B) – (3B² – 10B – 30B + 100) 3B x B – (3B² – 40B + 100)
= 3B² – 3B² + 40B – 100
Area of the path = 40B – 100
Given area of the path = 500 m²
40B – 100 = 50
40B = 500 + 100 = 600
B = 6004060040
B = 15m
Length of the field = 45 m..
Breadth of the field = 15 m..
ANsWeR :-
Let the length of the rectangular field = ‘L’ m
Breadth of the rectangular field = ‘B’ m
Area of the rectangular field = (L x B) m²
Also given :-
length = 3 x Breadth
Width of the path (W) = 5m
Length of the inner rectangle = L – 2W = l – 2(5) = 3B – 10m
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 x B) – (3B² – 10B – 30B + 100) 3B x B – (3B² – 40B + 100)
= 3B² – 3B² + 40B – 100
Area of the path = 40B – 100
Given area of the path = 500 m²
40B – 100 = 50
40B = 500 + 100 = 600
B = 6004060040
B = 15m
Length of the field = 45 m..
Breadth of the field = 15 m..