Question

floor, what fraction of the floor is uncovered ?
9. 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 m². Find the dimensions of the park.
8x
5x
1.5 m
[Hint. Let the length and the breadth of the plot be 8x and 5x metres respectively. Then
Area of the path = [(8x + 3) (5x + 3) - 40 x?] m² = (39x + 9) m?
Given: Area of the path = 594 m²: 39x + 9 = 594].​

Answer 1

★ Right 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 m² Find the dimensions of the park.

★ Answer ★

The length of the park is 120m and the breadth of the park is 75m

★ Given :-

• The Ratio of length and the breadth of a rectangular park are ↬ 8:5.
• A path is wide ↬ 1.5m
• Area of the park ↬ 594 m²

★Have to find :-

• What's the dimensions of the park.

★ Solution :-

So , first we consider

➤The length of the park ↬ " 8x " metres

➤The breadth of the park ↬ " 5x " metres

As we all know the park is in rectangular shape .

So ,

Area of the Rectangle ↬ length × Breadth

Now , substituting the values in the above formula :-

↬(8x × 5x) m²

= (40x²) m²

So , we include the path also in length =

(8x + 3) m.

Likewise include path in Breadth too =

(5x + 3)m.

Now,

Area of the park including the path =

(8x + 3)(5x + 3) m²

Simply, putting up the values :-

↬ (8x + 3)(5x + 40x²) m²

↬ (39x +9) m²

↬39x + 9 = 594

↬ 39x = 585

$\longmapsto\tt{x=\cancel\dfrac{585}{39}}$

$\longmapsto\tt{x=15}$

Therefore ,

↬ Length

• (8 x 15) m

= 120 m

↬ Breadth

• (5 x 15) m

= 75 m.

_______________________

Answer 2

$\huge\underline{\bf \orange{AnSweR :}}$

Area of the Rectangle ↬ length × Breadth

Now , substituting the values in the above formula :-

= (8x × 5x) m²

= (40x²) m²

So , we include the path also in length = (8x + 3) m.

Likewise include path in Breadth too = (5x + 3)m.

Now,

Area of the park including the path = (8x + 3)(5x + 3) m²

Simply, putting up the values :-

↬ (8x + 3)(5x + 40x²) m²

↬ (39x +9) m²

↬39x + 9 = 594

↬ 39x = 585

⟼x = 585/39

⟼x= 15

Therefore ,

↬ Length

(8 x 15) m

= 120 m Ans.

↬ Breadth

(5 x 15) m

= 75 m. Ans.