A triangle has side lengths of (x+4), (4x-8), and (2x+8) units. If the perimeter of the triangle is at least 88units, what is the minimum length of each side of the triangle?
oh that's easy you just equal everything to 88 units...
1. add everything together... so 7x+4
2. equal to 88
3. Solve!
7x+4=88
thenn... you have x to figure out each side
To find the minimum length of each side of the triangle, we need to determine the minimum value of the expressions (x+4), (4x-8), and (2x+8).
We know that the perimeter of the triangle is at least 88 units, so we can set up an inequality based on the sum of the side lengths:
(x+4) + (4x-8) + (2x+8) ≥ 88
Now, let's simplify the inequality:
7x + 4 ≥ 88
Subtracting 4 from both sides:
7x ≥ 84
Dividing both sides by 7:
x ≥ 12
Since x has to be greater than or equal to 12, we can substitute this value back into the expressions to find the minimum lengths of the sides:
(x+4) = (12+4) = 16 units
(4x-8) = (4*12-8) = 40 units
(2x+8) = (2*12+8) = 32 units
Therefore, the minimum length of each side of the triangle is 16 units, 40 units, and 32 units.