Math Problem Need Help? Thank You?

Question

I have a problem understanding this question( A rectangular building 100 m by 80 m is to be surrounded by a lawn of uniform width. the area of the lawn must be equal to the area of the building. Find the width of the lawn to the nearest tenth of a metre.) Thank You

Answer 1

ok. the area of the building is 80x100 = 8000sqm
you want a larger rectangle of turf equal width on all sides of the building. let's call it's dimensions h x w. you want h xw to equal 16,000sqm, so that the area of the grass to be 16,000(h x w) -8000 (area of building) = 8000 (same as area of building asked for in the problem)
but h and w are related in that h-100=w-80 because the problem specifies constant width around the building. solve for one of them,
w=h-20
and plug into an equation for area based on only one variable
h x (h-20) = 16,000
solve for h
h^2 - 20h -16,000 = 0
you can use the quadratic formula to solve, or intuitively
roughly (h-136.9)(h+116.9)=0
h will be about 136.9 (h can't be negative)
then the difference between the ha nd 100 is 36.9, and the width of the turf track would be 36.9/2

As I interpret the question they want to know the width from the building to the outer edge of a turf track with 'uniform width'. the solution in the answer above mine does not give uniform width for the track....
I don't take it to mean that they want the overall width of the plot of land.