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 path has an area of 594 m². Find the dimensions of the park. ​

Answer 1

Step-by-step Explanation:

Let the length of the park rectangle ABCD = 8y m

Let the breadth of the park rectangle ABCD = 5y m

Area of rectangle ABCD=(8y × 5y)m

                  =40y²m

Length of the park including path PQRS

                  =8y + 2(width of path)

                  =8y + 2(1.5)

                  = (8y + 3) m

The breadth of the park including path PQRS

                  = 5y + 2(width of path)

                  = 5y+2(1.5)

                  = (5y+3) m

Area of the park including path PQRS

                       = (8y + 3)(5y + 3)

                       = 40y + 24y + 15y + 9

simplyfying ⇒  (40y² + 39y + 9) m²

Given,

Area of the path=594m²

Area of PQRS - Area of ABCD = 594

  => (40y² + 39y + 9 ) −( 40y²) = 594

simplyfying => 39y + 9  = 594

                     =>  39y = 594 - 9

                     => 39y = 585

                     => y = 585​ / 39

                    => y = 15

     Length of the park = 8y

                    = 8 × 15

                    = 120m

      Breadth of the park = 5y

                     = 5 × 15

                     = 75m

The dimension of the park,

Length = 120 m.

Breadth = 75 m.

Answer 2

Given: Ratio of length and breadth of the park = 8 : 5

A path running all around the outside of the path = 1.5 m wide

Area of the path = 594 m².

To Find : Dimensions of the park.

Solution:

Let 8x and 5x be the length and breadth of the park.

Area of the park = Length x Breadth

Area of the park = (8x) x (5x) = 40x² m²

Length of the park and the path = (8x + 1.5 + 1.5) = (8x + 3 ) m²

Breadth of the park and the path = (5x + 1.5 + 1.5) = (5x + 3) m²

Area of the park and the path Length x Breadth

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

Area of the path = Area of the park and the path - Area of the park

(8x + 3) (5x + 3) - 40x² = 594

[Given: Area of the path is 594 m²]

40x² + 24x + 15x + 9 - 40x² = 594

39x + 9 = 594

39x = 594 - 9

39x = 585

x = 585/39

x = 15 m

Length of the park = 8x = 8 × 15 = 120 m

Breadth of the park = 5x = 5 × 15 = 75 m

Hence, the dimension of the park is 120 m by 75 m.

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