Triangle ABC is a right triangle such that m angle B= 90 degrees. If AC= 12 and BC=9, what is the perimeter of triangle ABC ? round to the nearest tenth.
Use the Pythagorean theorem.
(AB)^2 + (BC)^2 = (AC)^2
Insert the values in the equation above and solve for AB, then add the values for each side to get the perimeter.
To find the perimeter of the right triangle ABC, we need to find the length of the remaining side AB, using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, AC is the hypotenuse, so we have:
AC^2 = AB^2 + BC^2
Since AC = 12 and BC = 9, we can substitute those values in:
12^2 = AB^2 + 9^2
Simplifying this equation gives:
144 = AB^2 + 81
Subtracting 81 from both sides:
63 = AB^2
To find the length of AB, we need to take the square root of both sides:
√63 = √(AB^2)
Approximately:
7.94 = AB
Now that we have the lengths of all three sides (AB = 7.94, BC = 9, AC = 12), we can calculate the perimeter by adding the lengths of all three sides:
Perimeter = AB + BC + AC
Perimeter = 7.94 + 9 + 12
Perimeter = 29.94
Therefore, the perimeter of triangle ABC, rounded to the nearest tenth, is 29.9 units.