Question

The length and breadth of a a rectangular park are in the ratio 5:2. A 2.5m wide path running all around the outside ov the park has an area of 305m². Find the dimensions of the park

Answer 1

Solution

given

length of park = 305$m^{2}$

ratio of length and breadth = 5:2

width of park = 2.5m

let the length of  park be 5x

∴ breadth are 2x

so area= length × Breadth  

5x × 2x   =10x²

width of the all round the park=2.5m

∴lenght and breadth as well as path (5x+2.5 +2.5)m

=>   breadth of rectangular park=(5x+5)

=> (2x+2.5+2.5)=(2x+5)

space of the park=[(5x+2)(2x+5)-10x²]m²

=> (35x+25)m²

it is providing 35x +25 =305

⇒35x=280

=> x= 280/35

x=8

The lenght of th park=5 × 8=40m  

Breadth of the park=2× 8=16m

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@GauravSaxena01

Answer 2

Answer:

GIVEN THAT

RATIO OF LENGTH AND BREADTH OF THE RECTANGULAR PARK = 5:2

THEREFORE,

LENGTH = 5X

BREADTH=2X

THEN, AREA OF THE RECTANGLE=LENGTH*BREADTH

=>5X*2X

=>10X SQUARE

LENGTH OF THE OUTER PATH=5X+2.5+2.5

=>5x+5

BREADTH OF THE OUTER PATH=2X+2.5+2.5

=>2x+5

=>(5X+5)(2X+5)-10X SQUARE = 305 METRE SQUARE

=>10X SQUARE +25X +10X+25-10X SQUARE =305 METRE SQUARE

=>10X SQUARE AND 10X SQUARE WILL BE CANCELLED

=>35X+25=305METRE SQUARE

=>35X=305METRE SQUARE -25

=>35X=280

=>X=280/35

=>X=8

THEREFORE DIMENSIONS OF THE PARK IS (5*8),(2*8)

=40METRES AND 16 METRES

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