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 12 of this area, he would need to find 1 2 12 of the width and 1 2 12 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 12 of 1 square foot.

Answer:The answer in the procedureStep-by-step explanation:we know thatIf two figures are similar. then the ratio of its areas is equal to the scale factor squaredIn this problem we have a tile with a length of 1 foot by a width of 1 footThe area of the tile is equal to[tex]A=LW[/tex]substitute the values[tex]A=(1)(1)=1\ ft^{2}[/tex]Letz-------> the scale factorx------> the area of 1/2 tiley------> the area of the original tileso[tex]z^{2} =\frac{x}{y}[/tex]substitute[tex]z^{2} =\frac{(1/2)}{1}[/tex][tex]z=\frac{\sqrt{2}}{2}[/tex] -----> scale factorthereforeTo find the area of 1/2 tile must multiply the dimensions of the tile by the scale factorso[tex]L=1*\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}\ in[/tex][tex]W=1*\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}\ in[/tex]Calculate the area[tex]A=\frac{\sqrt{2}}{2}*\frac{\sqrt{2}}{2}=\frac{1}{2}\ ft^{2}[/tex]Martin's method is incorrect because to find the area of 1/2 tile, he multiplies the dimensions by 1/2so[tex]L=1*\frac{1}{2}=\frac{1}{2}\ in[/tex][tex]W=1*\frac{1}{2}=\frac{1}{2}\ in[/tex]the area will be[tex]A=\frac{1}{2}*\frac{1}{2}=\frac{1}{4}\ ft^{2}[/tex]