Solve the problem by writing and using a system of linear equations.
-The perimeter of a triangle is 29 inches. Three times the length of the longest side minus the length of the shortest side is 25 inches. The sum of the length of the longest side and twice the sum of both the other side lengths is 47 inches. Find the side lengths.
A) 8 in., 11 in., 10 in.
B) 7 in., 10 in., 12 in.
C) No solution
D) 8 in., 10 in., 11 in.

Question

Quizplus · Accepted Answer

Let the sides of the triangle be x, y, and z, with x being the longest side. The given information translates to the following system of equations:1. $x + y + z = 29$ (perimeter)2. $3x - z = 25$ (three times the longest side minus the shortest side)3. $x + 2(y + z) = 47$ (longest side plus twice the sum of the other sides)Solving this system, we find that the side lengths are 8 in., 10 in., and 11 in., which corresponds to option D.

Solve the Problem by Writing and Using a System of Linear