Question

if the area of square 3 is 80 cm squared in the area of square 2 is 100 cm squared what is the area of square one

Answer 1

We will first determine the sides of 2 & 3, that is:

`80=S^2_3\Rightarrow S_3=4\sqrt[]{5}`

And:

`100=S^2_2\Rightarrow S_2=10`

Where S2 and S3 are the sides of squares 1 and 2. From this we determine the side for square 1:

`S^2_2+S^2_3=S^2_1\Rightarrow(4\sqrt[]{5})^2+10^2=S^2_1\Rightarrow S_1=6\sqrt[]{5}`

Now, we determine the area of square 1, as follows:

`A_(s1)=(6\sqrt[]{5})^2\Rightarrow A_(s1)=180`

So, we have that the area of square 1 equals 180 squared units.