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
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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 m^2, find its width.
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.
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