The perimeter of a triangle is 18 feet. The second side is two feet longer than the first. The third side is two feet longer then the second. What are the lengths of the sides?

Question

Genesis Allen · Accepted Answer

Assuming the shortest side measures x, the second side would measure x + 2 and the third x +4, since the 3rd is 2 longer than the second.

x + 2 + 4 + x = 18. 3x plus 6 equals 18. 3 times is 12. x equals 4. Its sides are 4, 6, and 8 feet long.

Genesis Allen · Answer

Let the first side of the triangle be called A, the second side B and the third side C. Now, use the information from the problem to set up the equations ...

#A+B+C=18# #B = A+2# #C=B+2 = (A+2)+2=A+4# [ substitution from 2nd equation] Rewrite equation 1 now: #A+B+C=A+(A+2)+(A+4)=18# Make it simple... #3A+6=18# #3A=12# #A=4# Thus, side A equals 4. Apply this to the solutions for sides B and C. #B = A+2=4+2=6# #C=A+4=4+4=8# So, #DeltaABC# has sides #4,6, and 8#, respectively. I hope that was useful.

Julia Adams · Answer

undefined Let x represent the length of the first side. Then, the second side is x + 2 and the third side is (x + 2) + 2 = x + 4. The perimeter is the sum of the lengths of all three sides, which is given as 18 feet. So, the equation is: x + (x + 2) + (x + 4) = 18. Solving for x: 3x + 6 = 18. Subtracting 6 from both sides: 3x = 12. Dividing both sides by 3: x = 4. Therefore, the lengths of the sides are 4 feet, 6 feet, and 8 feet.