A triangle has sides of 10, 9, 13 cm. Can it be a right triangle? show work
To determine if a triangle is a right triangle, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's denote the sides of the triangle as follows:
a = 10 cm
b = 9 cm
c = 13 cm
Now, we can use the Pythagorean Theorem to determine if the triangle is a right triangle:
a^2 + b^2 = c^2
10^2 + 9^2 = 13^2
100 + 81 = 169
181 = 169
Since 181 is not equal to 169, the triangle does not satisfy the Pythagorean Theorem. Therefore, it is not a right triangle.
In conclusion, a triangle with sides of 10 cm, 9 cm, and 13 cm cannot be a right triangle.