A triangle has side lengths of (x+4), (4x-8), and (2x+8) units. If the perimeter of the triangle is at least 88 units, what is the minimum length of each side of the triangle?
The length of each side can be calculated by the distance formula.
For example, between (x+4) and (4x-8), the distance is:
sqrt((4x-x)^2+(-8-4)^2)
Sum the three sides and force the inequality of
∑lengths≥88.
Solve for x.
Note that the sides of the triangle are monotonically increasing, which means that the sum is also.
You can solve by an iterative process. I get x(min)=13.55...
So the lengths of each side can be calculated accordingly.
x+4 + 4x-8 + 2x+8 ≥ 88
7x + 4 ≥ 88
7x ≥ 84
x ≥ 12
plug x = 12 into each of the side expressions
Thanks Reiny, I wasn't reading the question right!
Sorry, Ashley, please go with Reiny's answer.
To find the minimum length of each side of the triangle, we need to consider the condition that the perimeter of the triangle is at least 88 units.
The perimeter of a triangle is the sum of the lengths of its sides. So, we need to set up an inequality using the given side lengths and solve for x.
Let's write the inequality for the perimeter:
(x+4) + (4x-8) + (2x+8) ≥ 88
Now, let's simplify and solve the inequality:
7x + 4 ≥ 88
Subtracting 4 from both sides:
7x ≥ 84
Dividing both sides by 7:
x ≥ 12
Since x represents a length, it cannot be negative, so we can conclude that x is greater than or equal to 12.
Now, let's find the minimum length of each side by plugging in the minimum value of x:
For the first side: (x+4) = (12+4) = 16 units
For the second side: (4x-8) = (4*12-8) = 40 units
For the third side: (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, respectively.