Algebra 2 word problem.

Question

The longest side of a triangle is 12 less than the sum of the other two sides. The shortest side is 10 more than one-half the third side. If the perimeter is 118, find each side and write the lengths in increasing order.

Answer 1

Set up variables for the three sides of the triangle.

 

Let the third side = x

Let the shortest side = 0.5x + 10

Let the longest side = (x + 0.5x + 10) - 12 = 1.5x - 2

 

The perimeter is the sum of the sides.

 

x + (0.5x + 10) + (1.5x - 2) = 118

 

Solve for x from this equation.  Once you solved for x, substitute that value into the variables to find the 3 sides.