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 Find the dimensions of the park.
Answers
➫ Correct 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.
➫ Given :-
→ The length and the breadth of a rectangular park are in the ratio 8:5.
→ A path, 1.5 m wide
→ area of the park is 594 m²
➫ To find :-
→ the dimensions of the park
➫ Solution :-
Let the length and the breadth of the park be 8x metres and 5x metres respectively.
⟹ Then, area of the park =(8x × 5x) m²
= (40x²) m²
⟹ Length of the park including the path =(8x + 3) m.
⟹ Breadth of the park including the path = (5x + 3)m.
⟹ Area of the park including the path =(8x + 3)(5x + 3) m²
⟹ Area of the path =[(8x + 3)(5x + 40x²]m²
=(39x +9) m²
39x + 9 = 594 = 39x =585
⟹ x = 585/39 =15.
⟹ length =(8 x 15) m = 120 m,
⟹ breadth =(5 x 15) m = 75 m.