If Boy 1 cuts half of a 30m by 40m lawn by cutting strips of equal width around the lawn. How wide should the width of the strips be so that the rectangle left that Boy 2 will have to cut is equal to the amount of lawn Boy 1 cut?

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Answer 1 · 2016-04-10T16:40:59

Width of strip should be 5 m

Tony B

Let area of the whole be #A#

Given that inner area - outer area = #A/2#

But #A=30xx40# so the inner area is such that:

#(30xx40)/2=(30-2x)(40-2x)#

#=>(30xx40)=2(1200-60x-80x+4x^2)#

#=>1200=2400-280x+8x^2#

Divide through out by 8

#150=300-35x+x^2#

#x^2-35x+150=0#

#(x-5)(x-30)=0#

#x=30 is not logical#

#=>x=5#

Width of strip should be 5 m
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Check:

Inner rectangle area #= (30-2(5))(40-2(5))#

#= 20xx30=600 m^2#

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Outer ring area

#=(40xx30) - 600 = 600 m^2#

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