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 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 1

The answer in the procedure

Explanation:

we know that

If two figures are similar. then the ratio of its areas is equal to the scale factor squared

In this problem we have a tile with a length of 1 foot by a width of 1 foot

The area of the tile is equal to

`A=LW`

substitute the values

`A=(1)(1)=1\ ft^(2)`

Let

z-------> the scale factor

x------> the area of 1/2 tile

y------> the area of the original tile

so

`z^(2) =(x)/(y)`

substitute

`z^(2) =((1/2))/(1)`

`z=(√(2))/(2)` -----> scale factor

therefore

To find the area of 1/2 tile must multiply the dimensions of the tile by the scale factor

so

`L=1*(√(2))/(2)=(√(2))/(2)\ in`

`W=1*(√(2))/(2)=(√(2))/(2)\ in`

Calculate the area

`A=(√(2))/(2)*(√(2))/(2)=(1)/(2)\ ft^(2)`

Martin's method is incorrect because to find the area of 1/2 tile, he multiplies the dimensions by 1/2

so

`L=1*(1)/(2)=(1)/(2)\ in`

`W=1*(1)/(2)=(1)/(2)\ in`

the area will be

`A=(1)/(2)*(1)/(2)=(1)/(4)\ ft^(2)`