Question

The length and the breadth of a rectangular park are in the ratio 8:5. A path, 1.5 m wide, running all around the outside of the park has an area of 594 m square. Find the dimensions of the park.​

Answer 1

Given that the ratio of length and breadth = 8 : 5

Let the length of the park be 8x

And the breadth of the park be 5x

Find the area of the park in term of x:

Area = Length x Breadth

Area = (8x) x (5x)  = 40x² m²

Find the Length and Breadth of the park and the path:

Length = 8x + 1.5 + 1.5 =  ( 8x + 3 ) m²

Breadth = 5x + 1.5 + 1.5 = (5x + 3) m²

Find the area of the park and the path:

Area = Length x Breadth

Area = (8x + 3) (5x + 3)  m²

Solve x:

Given that the area of the path is 594 m²

(8x + 3) (5x + 3)  - 40x² = 594

40x² + 24x + 15x + 9 - 40x² = 594

39x + 9 = 594

39x = 585

x = 15 m

Find the dimension of the park:

Length = 8x = 8(15) = 120 m

Breadth = 5x = 5(15) = 75 m

Answer 2

$\bf{\underline{Given}}:-$

• The length and breadth of a rectangular park are in the ratio 8:5.

• A path,1.5 m wide, running all around the outside of the park has an area of 594 m².

To find :-

• The dimensions of the park

Solution :-

Let the length of the plot be 8x m

and the breadth of the plot be 5x m

Area of the park = l × b

Area of the park = 8x × 5x

Area of the park = 40x² m²

Now,

• Length of the park including the path = (8x + 3)

• Breadth of the park including the path = (5x + 3)

Then,

Area of park including the path = (8x + 3)(5x + 3)

Area of park including the path = 8x(5x + 3) + 3(5x + 3)

Area of the park including the path = 40x² + 24x + 15x + 9

Area of park including the path = 40x² + 39x + 9

Area of the path = Area of park including the path - Area of the park

Area of the path = 40x² + 39x + 9 - 40x²

Area of the path = 39x + 9

According to the question,

⤇ 39x + 9 = 594

⤇ 39x = 594 - 9

⤇ 39x = 585

⤇ x = 585/39

⤇ x = 15

Hence,

• Length = 8x = 8 × 15 = 120 m

• breadth = 5x = 5 × 15 = 75 m