One side of triangle is 3 times the shortest side. The third side is 24 feet more than the shortest side. The perimeter is 109 . Find all three sides. The sides have lengths of , , and feet.

Question

One side of triangle is  times the shortest side. The third side is  feet more than the shortest side. The perimeter is . Find all three sides.The sides have lengths of , , and  feet.

Answer 1

Because there are three variables, you need three equations to solve this. First, let x, y, and z be the length of the sides with x being the shortest side. Let y be the side three times longer than the shortest side (x). Let z be 24 feet more than the shortest side (x). Our three equations then become: y = 3x, z = x + 24, and x + y + z = 109. Now use substitution to solve for x in the third equation. That gets you x + 3x + x + 24 = 109 which equals 5x = 109 - 24 or 5x = 85. From there you can divide 85 by 5 to see that x is 17. To get the other sides, plug in x = 17 to the other equations. y = 3x becomes y = 3(17) = 51. z = x + 24 becomes z = 17 + 24 = 41. The lengths of the sides of the triangle are 17, 41, and 51 feet.

Answer 2

s represents the length of the shortest side

3s represents the length of the second side

s + 24 represents the length of the third side

s + 3s + s + 24 = 109

Can you solve for s and answer?