Question

After studying the diagram shown, Michael makes the following conclusions:

Answer 1

Answer:

Therefore, Michael concludes option C)

C)$(DA)^{2}=(DG)^{2}+(AG)^{2}$

Step-by-step explanation:

Given:

1. DG = 3 and the area of square DEFG is 9.

2. AG = 4 and the area of square GHIA is 16.

3. DA = 5 and the area of square ABCD is 25.

So we have,

$(DG)^{2}=3^{2}=9\\ \\(AG)^{2}=4^{2}=16\\\\(DA)^{2}=5^{2}=25$

Now Add DG² and AG² we get

$(DG)^{2}+(AG)^{2}=9+16=25=(DA)^{2}$

Which is also called as  Pythagoras theorem i.e

$(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}$

Therefore, Michael concludes option C)

C)$(DA)^{2}=(DG)^{2}+(AG)^{2}$