3. The legs of a 45-45-90 right triangle both measure 7 cm . Find the length of the hypotenuse.

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse can be calculated using the formula \(x\sqrt{2}\), where \(x\) is the length of one leg. So, if both legs measure 7 cm, the hypotenuse would be \(7\sqrt{2}\) cm, which is approximately 9.9 cm. This relationship is not just a coincidence! It's a great example of the magic of geometry, helping to unlock the secrets of triangles. Whenever you're faced with a 45-45-90 triangle, remember this simple rule - it's a recipe for finding the hypotenuse that’s easy and delightful to apply.