Question

A path 5m wide rins along inside a rectangular field . The lengh of the rectangular field os three times the breadth of the field . If the area of the path is 500 meter square , then the length and breadth of the field.​

Answer 1

Question:-

A path 5m wide rins along inside a rectangular field . The lengh of the rectangular field os three times the breadth of the field . If the area of the path is 500 meter square , then the length and breadth of the field.

Answer:-

• The length and breadth of rectangle is 45 m and 15 m

To find:-

• Length and breadth of rectangular field

Solution:-

• Width of the path (w) = 5m

Let,

• Let the length of the rectangular field = ‘l’ m
• Breadth of the rectangular field = ‘b’ m

As we know,

$\large{ \boxed{ \red{ \sf { Area \: of \: the \: rectangular \: field = (l \times b) m²}}}}$

Also given ,

• length = 3 x Breadth
• L = 3b

INNER RECTANGLE,

• Length:-

$\large{ \rm : \implies \: \: \: \: \: \: \: length \: of \: inner \: rectangle =l \: – \: 2w}$

$\large{ \rm : \implies \: \: \: \: \: \: \: length \: of \: inner \: rectangle = l - 2(5)}$

$\large{ \rm : \implies \: \: \: \: \: \: \: length \: of \: inner \: rectangle = 3b- 10 \: m}$

• Breadth :-

$\large{ \rm : \implies \: \: \: \: \: \: \: breadth \: of \: inner \: rectangle = b \: – \: 2w}$

$\large{ \rm : \implies \: \: \: \: \: \: \: breadth \: of \: inner \: rectangle = b - 2(5)}$

$\large{ \rm : \implies \: \: \: \: \: \: \: breadth \: of \: inner \: rectangle = b - 10 \: m}$

• Area of inner rectangle :-

$\large{ \rm : \implies \: \: \: \: \: \: \: area \: of \: inner \: rectangle = (3b - 10)(b - 10)}$

$\large{ \rm : \implies \: \: \: \: \: \: \: area \: of \: inner \: rectangle =3 {b}^{2} - 10b - 30b + 100}$

Now,

• Area of the path = Area of outer rectangle – Area of inner rectangle

$\large{ \rm : \implies \: \: \: \: \: \: \: area \: of \:path =(l \times b) - (3 {b}^{2} - 10b - 30b + 100)}$

$\large{ \rm : \implies \: \: \: \: \: \: \: area \: of \:path =3b \times b - (3 {b}^{2} - 40b - 100)}$

$\large{ \rm : \implies \: \: \: \: \: \: \: area \: of \:path =3 {b}^{2} - 3 {b}^{2} + 40b - 100}$

$\large{ \rm : \implies \: \: \: \: \: \: \: area \: of \:path =40b - 100}$

Given,

• Area of the path = 500 m²

$\large{ \rm : \implies \: \: \: \: \: \: \: 40b - 100 = 500}$

$\large{ \rm : \implies \: \: \: \: \: \: \: 40b = 500 + 100 = 600}$

$\large{ \rm : \implies \: \: \: \: \: \: \: b = \frac{600}{40}}$

$\large{ \rm : \implies \: \: \: \: \: \: \: b = 15 \: m}$

Now,

• Length of the field =3b = 45 m
• Breadth of the field = 15 m

Hence,

The length and breadth of rectangle is 45 m and 15 m