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.
Answers
- [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:
Length = 120 meter
Breadth = 75 meter
Step-by-step explanation:
Let the length of the park rectangle ABCD be 8x meter
Let the breadth of the park rectangle ABCD be 5x meter
Area of rectangle ABCD = (8x × 5x) m
=40x² m
Length of the park including path PQRS
=8x + 2 (width of path)
=8x + 2 (1.5)
=8x + 3m
Breadth of the park including path PQRS
=5x + 2 (width of path)
=5x + 2 (1.5)
=5x + 3m
Area of the park including path PQRS
=(8x + 3)(5x + 3)
=(40x² + 39x + 9)m²
Given,
Area of the path=594m²
Area of PQRS - Area of ABCD = 594
=> 40x² + 39x + 9 − 40x = 594
=> 39x = 594 − 9
=> 39x = 585
=> x = 585/39
=> x = 15
Length of the park = 8x
= 8 × 15
= 120m
Breadth of the park=5x
= 5 × 15
= 75m