Question

47. A rectangular garden has an area 2000 m² and its length and breadth are in the ratio 5 : 4. A road of uniform width runs inside the garden around the perimeter and has an area 344 m², then the width of the road is​

Answer 1

Answer:

A rectangular garden has an area 2000 m² and its length and breadth are in the ratio 5 : 4. A road of uniform width runs inside the garden around the perimeter and has an area 344 m², then the width of the road is​ 2m.

Step-by-step explanation:

Given: Area of rectangular garden = 2000m²

Area of road = 344m²

Find:  The width of the road

Let the length and breadth of a rectangular garden be 5a m and 4a m respectively.

∴5a×4a=2000

$a^2 =100\\ a=10$

Hence, length of the garden =5×10=50m

and Breadth of the garden =4×10=40m

Let the uniform width of the road = x  m

∴ As per question,

50×40−[(50−2x)×(40−2x)]=344

$2000-2000+2x(50-40)-4x^2 =344\\ 4x^2 -180x+344=0\\ x^2 -45x+86=0\\x^2 -43x-2x+86=0$

x(x−43)−2(x−43)=0

⟹(x−43)(x−2)=0

∴x=2m