Question

The Pythagorean Theorem states that for any given right triangle, A^2 + B^2 = C^2. Using the Pythagorean Theorem, what should be the relationship between the areas of the three squares?

Answer 1

The areas of the two smaller squares, corresponding to the sides a and b of a right triangle, when combined, equal the area of the largest square corresponding to the hypotenuse, c, as per the Pythagorean Theorem.

Step-by-step explanation:

The relationship between the areas of the three squares in relation to the sides of a right triangle is an embodiment of the Pythagorean Theorem. Each square's area is calculated as the square of the length of the side it represents. Therefore, if we have a right triangle with sides a, b, and c, where c is the hypotenuse, the area of the square on side a would be a2, the area of the square on side b would be b2, and the area of the square on side c (the hypotenuse) would be c2. According to the Pythagorean theorem (a2 + b2 = c2), the areas of the two smaller squares (representing a2 and b2) when combined, should equal the area of the largest square (representing c2).