triangle length

Question

A certain triangle has a perimeter of 3093 mi the shortest side measures 72 mi less than the middle side and the longest side measures 378 mi more than the middle side find the length of the three sides

Answer 1

We can convert the side length relationships into algebraic equations to find a solution to this. Let S, M, and L be the lengths of the different sides of the triangle. Then:

S = M - 72 ( the shortest side measures 72 mi less than the middle side)

L = 378 + M (the longest side measures 378 mi more than the middle side)

L + M + S = 3093 (the sum of the triangle side lengths is the perimeter)

We can substitute the first and second equations into the third to solve for M.

(378 + M) + M + (M - 72) = 3093

3M + 306 = 3093

Next I subtract 306 from both sides of the equation.

3M = 2787

Then I divide by 3 on both sides:

M = 929 mi

We can then use the first equation to find S:

S = M - 72 = 929 - 72 = 857 mi

and the second equation to find L:

L = 378 + M = 378 + 929 = 1307 mi