set up help

Question

The perimeter of a triangle is 44 centimeters. Twice the length of the longest side minus the length of the shortest side is 30 centimeters. The sum of the length of the longest side and twice the sum of both the other side lengths is 68 centimeters. Find the side lengths.

Answer 1

Hi Heidi. Hope this answer helps. Assume that your three sides can each be represented by a variable. Let's call the longest side "L", the shortest side "s" and the other side "p". We know the perimeter is the sum of the three sides, so we can use these variables to create an equation a). a). L + s + p = 44 Now we know that "twice the length of the longest side minus the shortest side is 30. Let's create another equation. b) 2L - s = 30 Last, we know that the sum of the longest side and twice the sum of the other two sides is 68. so : c) L + 2(s+p) = 68 Now using these three equations we can solve for each individual side length. Substitute for L from equation a). to get -> L= 44-s-p. Now when you plug this into equation b), substitute this for L. so equation b) becomes: 2(44-s-p) -s = 30 However, you need to substitute for one of these variables to solve. Let's substitute for p. Using equation c). (44-s-p) + 2s + 2p =68. -> so 44+s+p=68 therefore p = 24-s. Now plug this back into equation b). You now have: 88-3s-2(24-s) = 30 you can now solve for s. Then use your equations for L to solve for L, given s. And lastly since you know the three sides add up to 44, you can solve for p. Let me know if this explains the set up.