Question

Use area of squares to visualize Pythagorean theorem

Answer 1

We know that the Pythagorean Theorem is a² + b² = c² and that the area of a square is l x w.

Firstly, we'll have to find the two measures of the triangle that correspond to the areas.

Since the figures are squares, we know that the length and width values must be the same.

We could square the numbers to find the side lengths, however we would have to square them again when substituting for the Pythagorean Theorem, so we can leave them as-is and adjust the equation accordingly.

(33) + b² = (44)

Next, we'll subtract our smaller value from our larger.

b² = (11)

Once again, we could find the square root of this number, but we'd just have to square it again to find the area of the square, so we can just simply write our answer as 11 units.

Therefore, the area of the square is 11 units!

Hope this helped! :)