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?

1 Answer
Apr 10, 2016

Width of strip should be 5 m

Explanation:

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
'~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check:

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

= 20xx30=600 m^2

'..........................................'
Outer ring area

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

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~