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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