Question

Writing  Find the length of the hypotenuse of the right triangle. Use pencil and paper. Explain how you can interpret the Pythagorean Theorem using the areas of squares. A right triangle has a vertical leg labeled 24 and a horizontal leg labeled 45. The hypotenuse is labeled c. 45 24 c ​(The figure is not drawn to​ scale.) The length of the hypotenuse is nothing. ​(Simplify your​ answer.)

Answer 1

To find the length of the hypotenuse of a right triangle, use the Pythagorean Theorem. In this case, the length of the hypotenuse, labeled c, is 51. The Pythagorean Theorem can be interpreted using the areas of squares.

Step-by-step explanation:

To find the length of the hypotenuse of a right triangle, we can use the Pythagorean Theorem. In this case, the theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, we have 24^2 + 45^2 = c^2. Simplifying this equation, we find that c^2 = 576 + 2025. Therefore, c^2 = 2601. Taking the square root of both sides of the equation, we get c = 51. So, the length of the hypotenuse, labelled c, is 51.

You can interpret the Pythagorean Theorem using the areas of squares by visualizing the sides of the right triangle as the lengths of squares. The areas of these squares correspond to the squares of the side lengths. The sum of the areas of the two smaller squares (a^2 + b^2) is equal to the area of the largest square (c^2).