A carpet is laid on the floor of a room 8 m by 5 m. There is a border

1.	A carpet is laid on the floor of a room 8 m by 5 m. There is a border of constant width all around the carpet. If the area of the border is 12 m2, find its width.
Answer» A carpet is laid on the floor of a room 8 m by 5 m. Area of the border = 12 m² Let the width of the carpet be x meter Area of floor = Length × Breadth = 8 × 5 = 40 m² Length without border = 8 m – (x + x) = (8 – 2x) m Breadth without border = 5 m – (x + x) m = (5 – 2x) m Area without border = Length without border × Breadth without border = (8 – 2x) × (5 – 2x) = 40 – 16x – 10x + 4x² Area of border = Area of floor – Area without border 12 = 40 – (40 – 16x – 10x + 4x²) or 4x² – 26x + 12 = 0 Solving above equation, we have (x– 6) (4x -2) = 0 x = 6 or x = 1/2 Since Border cannot be greater than carpet. Therefore, width of border is 1/2 m.

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

Answer»

A carpet is laid on the floor of a room 8 m by 5 m.

Area of the border = 12 m²

Let the width of the carpet be x meter

Area of floor = Length × Breadth

= 8 × 5

= 40 m²

Length without border = 8 m – (x + x) = (8 – 2x) m

Breadth without border = 5 m – (x + x) m = (5 – 2x) m

Area without border = Length without border × Breadth without border

= (8 – 2x) × (5 – 2x)

= 40 – 16x – 10x + 4x²

Area of border = Area of floor – Area without border

12 = 40 – (40 – 16x – 10x + 4x²)

or 4x² – 26x + 12 = 0

Solving above equation, we have

(x– 6) (4x -2) = 0

x = 6 or x = 1/2

Since Border cannot be greater than carpet.

Therefore, width of border is 1/2 m.