Question

Use the areas of two identical squares to to explain why [tex]5 ^{2} + 12 {}^{2} = 13 {}^{2}

A) By showing that the sum of the areas of two squares with side lengths 5 and 12 is equal to the area of a square with a side length of 13.
B) By demonstrating that 5 + 12 = 13.
C) By using the Pythagorean Theorem to prove that 52+122=132
52+122=132
D) By comparing the perimeters of two squares with side lengths 5 and 12.

Answer 1

Using the Pythagorean theorem, the sum of the areas of two squares with side lengths 5 and 12 is proven to equal the area of a square with a side length of 13, as 5^2 + 12^2 equals 13^2.

Step-by-step explanation:

To explain why 52 + 122 = 132 using the areas of two identical squares, we refer to the Pythagorean theorem. This theorem relates the lengths of the legs (a and b) of a right triangle with the length of the hypotenuse (c) by stating that a2 + b2 = c2.

For two squares with sides of lengths 5 and 12, their areas would be 25 and 144, respectively. According to the Pythagorean theorem, adding these areas should give us the area of the square with a side of length 13. Calculating the area of this third square gives us 169, which is indeed equal to 25+144. Therefore, 52 + 122 = 132 visually represents the areas of two squares completing the area of a larger square, consistent with the Pythagorean theorem.