SOLUTION: Please help me solve: One side of a triangle is 4 cm shorter than the base, x. The other side is 6 cm longer than the base. What lengths of the base will allow the perimeter of

Question 260259: Please help me solve:
One side of a triangle is 4 cm shorter than the base, x. The other side is 6 cm longer than the base. What lengths of the base will allow the perimeter of the triangle to be at least 29 cm? Use P = s1 + s2 + s3.
I must show the 5 steps for problem solving.
Thank you for your assistance!
Liz
Found 2 solutions by stanbon, drk:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
One side of a triangle is 4 cm shorter than the base, x. The other side is 6 cm longer than the base. What lengths of the base will allow the perimeter of the triangle to be at least 29 cm? Use P = s1 + s2 + s3.
-----
base: x
one side: x-4
other side: x+6
-----------------------
Inequality:
sum of sides >= 29 cm
x + x-4 + x+6 >= 29
3x+2 >= 29
3x >= 27
========================
x >= 9 cm
x-4 >= 5 cm
x+6 >= 15 cm
========================
Cheers,
Stan H.
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
I am not sure what 5 steps you use or your teacher wants, but here we go . . .
LABELS: x = base, x-4 = one side, x+6 = second side. Perimeter = a + b + c.
--
VERBAL MODEL - the sum of the three sides must be greater than or equal to 26.
--
ALGEBRAIC MODEL - x + x-4+x+6 >= 26
--
SOLVE:

combine like terms to get

subtract to get

divide to get

So,
x = 8,
x-4 = 4
x+6 = 14
--
However, these side length don't make a triangle. The first base value that does work is 11.
x = 11
x-4 = 7
x+6 = 17
---
CHECK
4+8+14 >= 26
16>= 26 [true].
However, these side length don't make a triangle.
11+7+17 >= 26
35>= 26 [true]
--
so you want 11, 7, 17 sides
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