Question

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

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.

What conclusion can he make about the sides (DG, AG, and DA) of the yellow triangle?
A) DG + AG = DA
B) DA - DG = AG
C) DA2 = DG2 + AG2
D) DA2 = DG2 - AG2

Answer 1

Therefore, Michael concludes option C)

C)
`(DA)^(2)=(DG)^(2)+(AG)^(2)`

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)`