Triangle AB is 12cm & BC is 15cm find length AC&perimeter
assuming that B is a right angle, AC = √369
If angle A is a right angle, then AC=9
if neither, there's no way to find the third side, given only the other two.
To find the length of AC in triangle ABC, you can use the Pythagorean theorem, which 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 lengths of the other two sides.
In this case, let's assume that angle ABC is a right angle. Since triangle ABC is not specified to be a right triangle, we will need to determine if it is a right triangle by checking if the given side lengths satisfy the Pythagorean theorem.
Let's label the sides of the triangle as follows:
AB = 12 cm (the side opposite angle A)
BC = 15 cm (the side opposite angle B)
AC = ? (the hypotenuse)
Using the Pythagorean theorem, we can write:
AB² + BC² = AC²
Substituting the given values:
12² + 15² = AC²
144 + 225 = AC²
369 = AC²
To find the length of AC, we take the square root of both sides:
AC = √369 ≈ 19.21 cm
So, the length of AC is approximately 19.21 cm.
To find the perimeter of triangle ABC, we add up the lengths of all three sides:
Perimeter = AB + BC + AC
Perimeter = 12 cm + 15 cm + 19.21 cm
Perimeter ≈ 46.21 cm
Therefore, the perimeter of triangle ABC is approximately 46.21 cm.