Answer:
Length of third side = 9
Explanation:
Because this is a right triangle, we can find the length of the third side using the Pythagorean theorem, which uses the equation a^2 + b^2 = c^2, where
- a and b are the lengths of the shortest sides called legs,
- and c is the length of the longest side called the hypotenuse (always opposite the right angle).
Thus, we can plug in 5 for a and √106 for c to find b, the length of the third side:
Step 1: Plug in 5 for a and √106 for for c. Then simplify:
5^2 + b^2 = (√106)^2
25 + b^2 = 106
Step 2: Subtract 25 from both sides:
(25 + b^2 = 106) - 25
b^2 = 81
Step 3: Take the square root of both sides to find b, the length of the third side:
√(b^2) = √81
b = ± 9
- Taking the square root of a number always gives both a positive and negative answer since squaring both a positive and negative answer yields a positive answer: Example: 4^2 = 16 and (-4)^2 = 16.
However, we can't have a negative side length so the third side is 9 units.