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 boarder is 12 m2 find its width.

Given:


Length = 8 m


Breadth = 5 m


Border = 12 m2


Let the width be x m



Area of floor = Length × Breadth


= 8 m × 5 m


= 40 m2


Now,


Length without border = 8 m - (x + x) m


= (8 – 2x) m


Breadth without border = 5 m - (x + x) m


= (5 – 2x) m


Therefore,


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)


⇒ 12 = 40 – 40 + 16x + 10x - 4x2


⇒ 12 = 26x - 4x2


⇒ 4x2 – 26x + 12 = 0


⇒ 4x2 – 24x – 2x + 12 = 0


⇒ 4x(x– 6) – 2(x -6) = 0


⇒ (x– 6) (4x -2) = 0


This gives us two equations,


i. x - 6 = 0


⇒ x = 6


ii. 4x -2 = 0


⇒ x = 1/2


Since,


Border cannot be greater than carpet


Hence, width of border is 1/2m = 50 cm


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