Question

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

Answer 1

Answer:

Let the common factor be 'x'.

Length of park without path

= 5x m

Breadth of park without path

= 2x m

Area of park without path

= (5×2)(x^2) sq.m

= 10(x^2) sq.m

Length of park with path

= (5x)+2×2.5 m

= 5x+10 m

Breadth of park with path

= (2x)+2×2.5 m

= 2x+10 m

Area of park with path

= (5x+10)(2x+10) sq.m

= 10(x^2)+(x)(2×10+5×10)+100 sq.m

= 10(x^2)+70x+100 sq.m

Now,

Area of path = 305 sq.m

or, 10(x^2)-10(x^2)+70x+100 = 305

or, 70x = 305-100 = 205

or, x = 205÷70 = 41/14

Length of park = 5×41÷14 m = 14.64 m(Approx.)

Breadth of park = 2×41÷14 m = 5.86 m(Approx.)

Thus,

Dimensions of park = 14.64 m × 5.86 m(Answer)