The length and the breadth of a rectangular Park are in the ratio 5:2,a 2.5 m wide path running all around the outside of the park has an area of 305 sq. m. find the length and breadth of the park.

Given that :-the length and the breadth of a rectangular Park are in the ratio 5:2,a 2.5 m wide path running all around the outside of the park has an area of 305 sq.mNeed to Find :-Dimensions of parkSolution :-

Let the length be 5x and breadth be 2x

Now,Area = Length × BreadthArea = 5x × 2xArea = 10x²Now,

When 2.5 m added both sides

New Length = (5x + 2.5 + 2.5) = (5x + 5) m

New Breadth = (2x + 2.5 + 2.5) = (2x + 5) m

Now,Area of park = (5x + 5) × (2x + 5)305 = (10x² + 25x + 10x + 25)305 = (10x² + 35x + 25)305 = 10x² + 35x + 25 - 10x²305 = 35x + 25305 - 25 = 35x35x = 280x = 8.°. Length = 5(8) = 40 m.°. Breadth = 3(8) = 24 m