Question

A triangle has side lengths of (5.8k+3.3m)(5.8k+3.3m) centimeters, (8.4k-2.4n)(8.4k−2.4n) centimeters, and (7.9n-4.4m)(7.9n−4.4m) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

Answer 1

(14.2k - 1.1m + 5.5n) cm

Explanation:

Perimeter of a triangle = side A + side B + side C

Side A = (5.8k+3.3m)cm

Side B = (8.4k-2.4n)cm

Side C = (7.9n-4.4m)cm

Perimeter of a triangle = side A + side B + side C

= (5.8k+3.3m) + (8.4k-2.4n) + (7.9n-4.4m)

= 5.8k + 3.3m + 8.4k - 2.4n + 7.9n - 4.4m

Collect like terms

= 5.8k + 8.4k + 3.3m - 4.4m - 2.4n + 7.9n

= (14.2k - 1.1m + 5.5n) cm

Therefore, the perimeter of the triangle = (14.2k - 1.1m + 5.5n) cm