Question

A carpet is laid on the floor of a room 8m by 5m. There is a border of constant width all around the carpet. If the area of the border is 12 m², find its width.

Answer 1

Area of border = 12 m²

Length of room = 8m

Breadth of room = 5m

Let x be the width of carpet

Length of carpet = 8-x-x = (8-2x)m

Breadth of carpet = 5-x-x = (5-2x)m

Area of room (carpet + border) = 8 x 5 = 40 m²

Area of carpet = (8-2x)(5-2x)

= (40-16x-10x+4x²)

= (4x²-26x+40)

Now,

Area of ground = Area of border + Area of carpet

40 = 12 + 4x²-26x+40

2x²-13x+6 = 0

After solving above equation, we have

x = 1/2 or x = 6 (ignore as it is longer than room)

So, Width of border = 0.5m