The perimeter of a triangle is 29 inches. Three times the length of the longest side minus the length of the shortest side is 53 inches. The sum of the length of the longest side and three times the sum of both the other side lengths is 49 inches. Find the side lengths.
A) 4 in., 6 in., 19 in.
B) 4 in., 7 in., 18 in.
C) 3 in., 6 in., 20 in.
D) No solution

Question

Quizplus · Accepted Answer

Let the sides of the triangle be x, y, and z, with z being the longest side. The given conditions are:1. $x + y + z = 29$ (perimeter)2. $3z - x = 53$3. $z + 3(x + y) = 49$From (1), we can express $y = 29 - x - z$.Substituting $y$ in (3) gives $z + 3(29 - z) = 49$, simplifying to $z + 87 - 3z = 49$, which leads to $2z = 38$, so $z = 19$.Substituting $z = 19$ in (2) gives $3(19) - x = 53$, which simplifies to $57 - x = 53$, so $x = 4$.Finally, substituting $x = 4$ and $z = 19$ in $x + y + z = 29$ gives $4 + y + 19 = 29$, so $y = 6$.Therefore, the side lengths are 4 in., 6 in., and 19 in.

The Perimeter of a Triangle Is 29 Inches