The diagram shows squares 1,2, and 3 constructed on the sides of a right triangle. Which statement about the squares must be true?

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.

answer: options

step-by-step explanation: