Question

A rectangular floor measuring 15 m by 12 m is to be laid with a carpet leaving a gap
of 2 m all round the carpet. Find the area of the carpet?

Answer 1

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Let width of carpet be 'x'm

Therefore, inclusive of border:

Length of room = 8m

Breadth of room = 5m

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

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

Area of room (carpet + border) 

=  8*5 = 40sq.m

Area of just carpet

= (8-2x)(5-2x)

= (40-16x-10x+4x^2)

= (4x^2-26x+40)sq.m

Area of just border = 12sq.m (given)

Therefore,

Area of ground = Area of just border + Area of just carpet

=> 40 = 12+(4x^2-26x+40)

=> 0 = 4x^2-26x+12

=> 0 = 2x^2-13x+6 (dividing equation by 2)

=> 0 = 2x^2-12x-x+6

=> 0 = 2x(x-6)-1(x-6)

=> 0 = (2x-1)(x-6)

=> x = 1/2 = 0.5m or 6m

discarding 6m since it is longer than room then

Therefore, width of border = 0.5m

Answer 2

Let width of carpet be 'x'm

Therefore, inclusive of border:

Length of room = 8m

Breadth of room = 5m

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

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

Area of room (carpet + border)

= 8*5 = 40sq.m

Area of just carpet

= (8-2x)(5-2x)

= (40-16x-10x+4x^2)

= (4x^2-26x+40)sq.m

Area of just border = 12sq.m (given)

Therefore,

Area of ground = Area of just border + Area of just carpet

=> 40 = 12+(4x^2-26x+40)

=> 0 = 4x^2-26x+12

=> 0 = 2x^2-13x+6 (dividing equation by 2)

=> 0 = 2x^2-12x-x+6

=> 0 = 2x(x-6)-1(x-6)

=> 0 = (2x-1)(x-6)

=> x = 1/2 = 0.5m or 6m

discarding 6m since it is longer than room then

Therefore, width of border = 0.5m