SOLUTION: One side of triangle is half the longest side. The third side is 9 feet less than the longest side. The perimeter is 51. Find all three sides.

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Question 969383: One side of triangle is half the longest side. The third side is 9 feet less than the longest side. The perimeter is 51. Find all three sides.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
x, y, z, in that order;
x=z%2F2;
y=-9%2Bz;
x%2By%2Bz=51
-
Assumed z is the longest side. The third side is y.


Substitute for x and y in the perimeter equation.
z%2F2%2Bz-9%2Bz=51
z%2F2%2B2z-9=51
z%2F2%2B2z=60
z%2B4z=120
5z=120
highlight%28z=24%29

Find the others.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

One side of triangle is half the longest side. The third side is 9 feet less than the longest side. The perimeter is 51. Find all three sides.
Let the 1st side be F

Then longest side = 2F, and 3rd side = 2F - 9

We then get: F + 2F + 2F - 9 = 51

5F - 9 = 51

5F = 51 + 9

5F = 60

F, or 1st side = 60%2F5, or highlight_green%2812%29 ft

Longest side: 2(12), or highlight_green%2824%29 ft

3rd side = 2(12) - 9, or 24 - 9, or highlight_green%2815%29 ft