Question

The length and breadth of a rectangular park are in the ratio of 8:5. a path 2m wide,running all around outside park has area of 640 m sqr. find dimension of park

Answer 1

If the area is 640 sq m then,

let the length of the rectangular park be 8x
∴ breadth will be 5x
so area= l*b
                8x*5x
             =40x²
width of the park all around the park=2m
∴lenght and breadth including path (8x+2 +2)m
=(8x+4) and breadth of rectangular park
=(5x+2+2)
=(5x+4)
thus, area of the park=[(8x+4)(5x+4)-40x².]m²
=(35x+25)m²
it is given that 35x +25 =305
⇒35x=280
x=8
thus the lenght of th park=5*8=40m and breadth of the park=2*8=16m

Answer 2

$\bf{\mathsf{\mathtt{\huge{SOLUTION;-}}}}$

$\bf{\mathsf{\mathtt{GIVEN:-}}}$

$\implies{\tiny{ \mathsf{Let \: \: the \: \: Length \: be \: 8x \: metres}}} \\ \\ \ \implies{ \mathsf{\tiny{Let \: \: the \: \: Breadth \: be \: 5x \: metres}}} \\ \: \: \\ { \implies\mathsf{ \tiny{then, \: Area \: of \: \: the \: Park = (8x \times 5x)}}} \\ \\ { \implies\mathsf{ \fbox{ \tiny{ {40x}^{2}}}}} \\ \\ \implies{\mathsf{ \tiny{Length \: of \: the \: Park \: including \: the \: park = (8x + 5)}}} \\ \\ \\ \implies{\mathsf{ \tiny{Length \: of \: the \: Park \: including \: the \: path = (5x + 4)}}} \\ \\ \\ \\ \implies{ \mathsf{ \tiny{Area \: \: of \: the \: Park \: including \: the \: path = (8x + 4)(5x + 4) {m}^{2} }}} \\ \\ \\ \implies{ \mathsf{ \tiny{Area \: \: of \: the \: Park \: including \: the \: path = (8x + 4)(5x + 4) - {40x} \: ^{2}) {m}^{2} }}} \\ \\ \\ \\ \implies{ \tiny{ \tiny{ \cancel{{40x}^{2}}} + 32x + 20x + 16 - \cancel{{40x}^{2}}}} \\ \\ \\ \implies{ \tiny{ \mathsf{(52x + 16) \: {m}^{2} }}} \\ \\ \\ \implies{ \tiny{ \mathsf{(52x + 16) = 640 }}} \\ \\ \\ \implies{ \tiny{ \mathsf{(52x ) = 640 - 16 }}} \\ \\ \\ \implies{ \mathsf{ \tiny{x = \frac{624}{52} = 12.00}}} \\ \\ \ \mathsf{ \bf{ \fbox{Conclusion - }}} \\ \\ \\ \\ \implies{ \mathsf{ \tiny{Length\: \: of \: the \: park = (8 \times 12)m = 96 metres}}} \\ \\ \\ \\ \implies{ \mathsf{ \tiny{Breadth\: \: of \: the \: park = (5 \times 12)m = 60metres}}}$