Problem: One side of triangle is 7 more than 3 times the shortest side. The third side is 24 centimeters more than the shortest side. The perimeter is 111. Find all three sides.
Analysis: A triangle has three sides. The length of the perimeter is the sum of the lengths of the three sides. This problem gives the perimeter and the length of two sides in terms of the shortest side.
Assign variables: Let x=length of shortest side [when possible, assign variable(s) to the value the problem asks you to find]. We could assign variables to the other two sides or we could just insert the expressions when needed (let's do that).
Translate:
"One side of triangle is 7 more than 3 times the shortest side" means
Side1 = 7 + 3 * x
"third side is 24 centimeters more than the shortest side" means
Side3 = 24 + x
So, Side2 must be the shortest side (we called x).
O.K., now the math:
Side1 + Side2 + Side3 = 111
(3x + 7) + x + (x+24) = 111 [rewritten]
5x + 31 = 111 [collect terms]
5x = 80 [subtract 31 from both sides]
x = 16 [divide both sides by 5]
Side1= 3(16)+7 = 55
Side2=x=16
Side3 = 40
Perimeter = 55+16+40 = 111 check!
