A carpet is laid on the floor of a room 8 m by 5 m There is a border of constant width all around th...

Question

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

Accepted Answer

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

Area of the border = 12 m^2

Let the width of the carpet be x meter

Area of floor = Length × Breadth

= 8 × 5

= 40 m^2

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 + 4x^2

Area of border = Area of the floor - Area without border

12 = 40 – (40 – 16x – 10x + 4x^2)

or 4x^2 – 26x + 12 = 0

Solving the above equation, we have

(x– 6) (4x -2) = 0

x = 6 or x = 1/2

Border cannot be greater than the carpet.

Therefore, the width of the border is 1/2 m.

RS Aggarwal Solutions Class 10 Mathematics Solutions for Perimeter And Area Of Plane Figures Exercise 15B in Chapter 15 - Perimeter And Area Of Plane Figures