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 594m² find the dimensions of the park​

Answer 1

Answer:

Let the length of the park rectangle ABCD be 8x m

Let the breadth of the park rectangle ABCD be 5x m

Area of rectangle ABCD=(8x×5x)m

=40x

2

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)

=(40x

2

+39x+9)m

2

Given,

Area of the path=594m

2

Area of PQRS-Area of ABCD=594

=>40x

2

+39x+9−40x

2

=594

=>39x=594−9

=>39x=585

=>x=

39

585

=>x=15

Length of the park=8x

=8×15

=120m

Breadth of the park=5x

=5×15

=75m