Answer:
Unlabeled side length = 15.00 units
Explanation:
Because this is a right triangle, we can find the unlabeled side length using the Pythagorean theorem, which is
a^2 + b^2 = c^2, where
- a and b are the shorter sides called legs,
- and c is the longest side called the hypotenuse.
In the triangle, we're given that the legs are 12 and 9 units and the unlabeled side is the hypotenuse, which we must find:
Step 1: Plug in 12 for a and 9 for b and simplify:
12^2 + 9^2 = c^2
144 + 81 = c^2
225 = c^2
Step 2: Take the square root of both sides to solve for c, the hypotenuse (aka the unlabeled side):
± √225 = √(c)^2
± 15 = c
15.00 units = c
Although taking the square root of a number produced both a positive and negative answer since squaring both a positive and negative answer gives us a positive answer (e..g, 15 * 15 = 225 and -15 * -15 = 225), you can't have a negative measure. Therefore, c, the unlabeled side length = 15.00 units.