Hello there! The length of the hypotenuse of a right triangle whose legs have lengths 12 cm and 16 cm is 20 cm, or the square root of 400 cm.
In Pythagorean Theorem, the hypotenuse of a right triangle is always the longest side and is representative of a variable we know as c^2, or c squared. Since we know that the right triangle in this problem has lengths 12 cm and 16 cm, we know that a^2 equals 12 squared and b^2 equals 16 squared. Because the formula for Pythagorean Theorem is a^2 + b^2 = c^2, we can write our problem out:
12^2 + 16^2 = c^2
12^2 (or 12 squared) equals 144 since 12 x 12 = 144
16^2 (or 16 squared) equals 256 since 16 x 16 = 256
Since we know what a squared and b squared equal, we can add them to find what our hypotenuse squared is.
144 + 256 = 400
We now know that our hypotenuse squared equals 400. To find c, we can simply find the square root of 400. You can keep this question in mind when doing it: “What number can be multiplied by itself to get 400?”
When calculating, we will find that the square root of 400 is 20. To verify, we can multiply 20 by itself to see what we get.
20 x 20 = 400
Our equation is true! Therefore, here is your final equation:
12^2 + 16^2 = 20^2
The length of the hypotenuse is 20 cm. If you need any extra help, let me know and I will gladly assist you.
