A path 5 m wide runs along the inside of the rectangular field. The le

1.	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.
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 L = 3B 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 = \(\frac{600}{40}\) B = 15m Length of the field = 45 m; Breadth of the field = 15 m

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.

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

L = 3B

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 = \(\frac{600}{40}\)

B = 15m

Length of the field = 45 m;

Breadth of the field = 15 m