Question

You have learned about special right triangles. Using that knowledge, you decide to take a square cake with 10-inch sides and divide it diagonally to form two special right triangles. Find and explain how you know the exact (no decimals) measure of the hypotenuse.
Now find the exact diagonal measure of cakes that are an 8-inch square, a 12-inch square, and a 15-inch square.
Did you discover a shortcut that works with any square cake? Explain.

Please show your work

Answer 1

Check the picture below.

thus, using  the 45-45-90 rule, for a square with sides if 8-inch, h = 8√(2), for 12-inch sides, h = 12√(2), for 15-inch sides, h = 15√(2), and so on.