Question

Martin says the area of a tile with a length of 1 foot by a width of 1 foot has an area of 1 square foot. And, to find 1/2 of this area, he would need to find 1/2 of the width and 1/2 of the length, and then multiply those two values. Unfortunately, his method is incorrect. Show at least one equation to show why this method would not work, and briefly state a method that will find 1/2 of 1 square foot.

Answer 1

His method is incorrect. By finding 1/2 the width and 1/2 the length, if we multiply them , we would get 1/4 of the original area.

Area = 0.5*l*0.5*w = 0.25*l*w = l*w/4

Let us establish

length = l

width = w

Original Area = l*w

Half the area = (a*l)*(b*w) = 0.5*(l*w)

This means that

a*b = 0.5

if b is equal to a, then

a = √0.5 = √2/2 = 0.707

Then, if a factor of a, where to be introduced in the lenght and width of the tile, we would obtain half the area.