Question 4751
Draw a rectangle, 40x30. Draw another rectangle inside this one. Let the width of grass cut by Ric be x.


So, we know several things now: total area = 40x30 = 1200


Darin area is (40-2x)(30-2x) which multiplies out and simplifies to {{{4x^2-140x+1200}}}. Now this has to be half the total area, so must equal 600.


{{{4x^2-140x+1200 = 600}}} and simplifying gives {{{x^2-35x+150 = 0}}}. Now this is the equation we need to solve to find x. It factorises nicely into (x-30)(x-5) = 0, so x is either 30 or 5. Now x=30 is not a physically correct answer to your question, so x=5


Thinking about this, lets have a look at the smaller rectangle: (40-2x)(30-2x) becomes (40-10)(30-10) --> 30x20 which is 600, which half of 1200, so correct.


jon.