The following formula gives the perimeter \( P \) of a triangle with sides \( a, b \), and \( c \). \[ P=a+b+c \] Find the perimeter of a triangle with side lengths 2,9 , and 12 .

To find the perimeter of the triangle, simply plug in the side lengths into the formula \( P = a + b + c \). Here, \( a = 2 \), \( b = 9 \), and \( c = 12 \). So we have: \[ P = 2 + 9 + 12 = 23 \] Therefore, the perimeter of the triangle is 23 units! Triangles have a fascinating history! The ancient Greeks were keen observers of geometric principles, and they studied triangles extensively, particularly through the work of Euclid, who introduced the concept of geometry in his work "Elements." Triangles were so important because they help understand basic shapes and the foundations of geometry. If you're looking to calculate the perimeter of triangles more efficiently, remember to always verify the lengths first! A quick pit stop at the triangle inequality theorem can save you from basic mistakes—where the sum of any two sides must exceed the length of the third side. For example, for sides 2, 9, and 12: \( 2 + 9 = 11 < 12 \), which means these cannot form a triangle, so ensure your sides actually make a triangle before calculating the perimeter!