SOLUTION: One side of triangle is half the longest side. The third side is 7 feet less than the longest side. The perimeter is 78. Find all three sides.

Algebra ->  Triangles -> SOLUTION: One side of triangle is half the longest side. The third side is 7 feet less than the longest side. The perimeter is 78. Find all three sides.      Log On


   

Question 910410: One side of triangle is half the longest side. The third side is 7 feet less than the longest side. The perimeter is 78. Find all three sides.
Found 2 solutions by FaroukHarb, ewatrrr:
Answer by FaroukHarb(6) About Me  (Show Source):
You can put this solution on YOUR website!
If you call the longest side (x) Then the second side is 1/2(x) and the third side is x - 7. The sum of these three sides is 78 so this translates algebraically to:
x + 1/2 x + x - 7 = 78
2.5x = 85
x = 34 feet
so the longest side is 34 feet and the second side is 1/2 x = 17 feet and the third side is x - 7 = 27 feet so the triangle's three sides are
34,17, 27

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
x the longest side
x%2F2+%2B+x+%2B%28x-7%29++=+78 |Multiplying thru by 2 so as all denominators = 1
x + 2x + 2(x-7) = 156
x + 2x + 2x - 14= 156
5x = 170
x = 34
Sides: 17, 34, 27
and checking..
17 + 34 + 27 = 78