Answer:
Option D.
Step-by-step explanation:
Remember the Pythagorean theorem.
For a triangle rectangle of catheti A and B, and hypotenuse H, we have:
A^2 + B^2 = H^2
Now, also remember that for a square of sidelength L the area is:
area = L^2
First, you can see that square 1 has a side length equal to one of the catheti, and the same for square 2. While square 3 has a side lenght equal to the hypotenuse of the triangle.
If we define:
A = length of the smaller cathetus
then the area of square 1 is:
A^2
B = length of the larger cathetus.
The area of square 2 is then:
B^2
H as the length of the hypotenuse:
The area of square 3 is:
H^2
And by Pythagorean theorem we know that:
A^2 + B^2 = H^2
We can replace these by:
area of square 1 + area of square 2 = area of square 3.
Then the correct option is D.
