Question

the length and breadth of a park are in the ratio of 5:2. a wide path of 2m width around the park has an area 445m². find the dimensions of the park​

Answer 1

Given :-

Ratio of length and breath of a park = 5 : 2

Width of the park around = 2 m

Area of the path = 445 m²

To Find :-

The length of the park.

The breadth of the park.

Solution :-

We know that,

• l = Length
• b = Breadth
• a = Area

Consider common ratio as 'x'. Then the length and breadth of the park would be '5x' and '2x' respectively.

By the formula,

$\underline{\boxed{\sf Area \ of \ rectangle=Length \times Breadth}}$

Substituting their values,

5x × 2x = 10x

Given that, Width of the park around = 2 m

The dimensions,

Length of rectangle including the path = 5x + 2 + 2

Length = 5x + 4

Breadth of rectangle including the path = 2x + 2 + 2

Breadth = 2x + 4

By the formula,

Area of rectangle = Length × Breadth

Substituting them,

Area = (5x + 4) × (2x + 4)

Area = 10x² + 20x + 8x + 16

According to the question,

Area of the path = Area of the rectangle including the path - Area of the smaller rectangle

By substituting,

Area of the path = [(10x² + 20x + 8x + 16) - 10x²]

445 = 44x + 16

By transposing,

44x = 445 - 16

44x = 429

x = 429/44

x = 9.75

Dimensions would be,

Length (l) = 5 × 9.75 = 48.75 m

Breadth (b) = 2 × 9.75 = 19.5 m

Therefore, the dimensions are 48.75 × 19.5 m.