Questions: The perimeter is found by adding all of the sides together. If the perimeter of the triangle below is 42, find x.

Solution Steps

The problem states that the perimeter of the triangle is 42, and the lengths of two sides are given as 6 and 8.

Since the triangle is a right triangle, we can use the Pythagorean theorem: \[ a^2 + b^2 = c^2 \] where \( a = 6 \) and \( b = 8 \).

\[ 6^2 + 8^2 = c^2 \] \[ 36 + 64 = c^2 \] \[ 100 = c^2 \] \[ c = \sqrt{100} \] \[ c = 10 \]

The perimeter is the sum of all sides: \[ 6 + 8 + 10 = 24 \]

Final Answer