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

1.	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» $\bf{\underline{Given}}:-$ 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

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»

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

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