Question

7. The length and breadth of a garden are in the ratio 5:2. A path 2.5 m wide runs
along the boundary of the garden outside. If the area of the path is 305 m², find the
area of the garden.​

Answer 1

Answer:

Step-by-step explanation:

Given that area of the park be 305m^2.

Let the length of the park be 5x m and breadth be 2x m.

Therefore,

Area of the rectangular park = (5x) x (2x)

= 10x^2 m^2

Width of the path = 2.5 m  

From the figure,

Outer length PQ = 5x m + 2.5 m + 2.5 m

= (5x + 5) m

Outer breadth QR = 2x + 2.5 m + 2.5 m

= (2x + 5) m

Area of PQRS = (5x + 5) m x (2x + 5) m

=(10x2 + 25x + 10x + 25) m^2

= (10x2 + 35x + 25) m^2

Area of the path = [(10x^2 + 35x + 25) – 10x^2] m^2

By solving above equation we get

305 = 35x + 25

305 – 25 = 35x

280 = 35x

x = 280/35 = 8

Therefore,

Length of the park = 5x

= 5 x 8 = 40 m

Breadth of the park = 2x

= 2 x 8 = 16 m

Answer 2

Answer:

length =5.2

breath =2.5

perimeter =2(length+breath)

p=2(5.2+2.5)

p = 2*7.7

p = 15.4