SOLUTION: the first side of a triangle is 7cm shorter thatn twice the second side. the third side is 4cm longer than the first side. the perimeter is 80. find the length of each side. please

Question 13187: the first side of a triangle is 7cm shorter thatn twice the second side. the third side is 4cm longer than the first side. the perimeter is 80. find the length of each side. please help me out with these problems.
Answer by akmb1215(68) (Show Source): You can put this solution on YOUR website!
The first thing to do is to assign variables for the sides of the triangle. I am going to call them X, Y, and Z. The first side, X, is 7cm shorter than twice the second side, Y. Written as an equation, this is . Then, you know that the third side, Z, is 4cm longer than the first side. WRite as an equation, this is . The perimeter, which is the sides added together, is 80. So, .
To solve this, you will need to figure out a way to get X + Y + Z = 80 to have only 1 variable in it. Since you know that Z = X + 4, you can plug X + 4 in for Z in that equation. Now you have . For the first equation we wrote, solve for Y, which makes the equation . Now plug this in for Y in the longer equation, which changes it to . To solve the equation, add like terms, which changes the equation to . Move the 11 to the right side of the equation, which is . Solve for X (X = 23). To figure out Y and Z, simply plug 23 in for X in the original equations. ; Y=30. ; Z=27.
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