Question

The perimeter of an equilateral triangle must be at most 195 feet. Create an inequality to represent what the side lengths of the triangle must be. Solve the inequality and explain each of your steps. Graph your solutions on a number line. Explain what jpur solution means.

Answer 1

Let's denote the side length of the equilateral triangle as "s" in feet. An equilateral triangle has all sides of equal length. The perimeter (P) of an equilateral triangle is the sum of its three sides, which can be expressed as:

P = 3s

Given that the perimeter must be at most 195 feet, we can create the following inequality:

3s ≤ 195

Now, let's solve this inequality step by step:

1. Divide both sides of the inequality by 3 to isolate "s" (the side length):

(3s) / 3 ≤ 195 / 3

s ≤ 65

So, the inequality is:

s ≤ 65

This inequality represents that the side length (s) of the equilateral triangle must be less than or equal to 65 feet. In other words, the maximum side length for the equilateral triangle is 65 feet to ensure that the perimeter does not exceed 195 feet.

To graph the solution on a number line, you would plot a closed circle (≤) at 65, indicating that 65 is included in the solution set, and shade the region to the left to represent all side lengths less than or equal to 65 feet.

This solution means that to have an equilateral triangle with a perimeter at most 195 feet, the side length must be 65 feet or less. If the side length exceeds 65 feet, the perimeter would be greater than 195 feet, which does not meet the given condition.

Explanation:

Answer 2

x ≤ 65 and x ≥ 0

Explanation:

The perimeter of a shape is found by adding the lengths of all sides of that shape.

So, if we know the perimeter of a triangle is found by adding the lengths of all the sides together, the perimeter of this triangle can be represented as: Side 1 + Side 2 + Side 3 ≤ 195. (Since the perimeter cannot be more than 195 feet, as stated in the question).

However, we know this triangle is equilateral from the question, and an equilateral triangle is a triangle that has all three sides lengths as equal. So:

Side 1 = Side 2 = Side 3

Since we know all of these side lengths are equal, we can represent them using a variable, for this example let's use 'x'. We'll say that the side length of each side of this triangle is x. ( x = Side 1 = Side 2 + Side 3).

Now, Let's plug x into the equation I mentioned earlier:

Side 1 + Side 2 + Side 3 ≤ 195

x + x + x ≤ 195

(simplify:)

3x ≤ 195

Now, the question asks us to solve the inequality. This means it is asking us to find what x is. So we can simply solve the equation for x:

3x ≤ 195

(divide both sides by 3)

x ≤ 65

However, it is also important to note that since x represents the length of something, it cannot be negative (just like how if someone asks how tall you are, you can't be a "negative height").

So, x ≥ 0

(however, I'm not sure if your teacher will require you write this part, she might just want you to know the first part).

Finally, the question asks us to graph our solution on a number line. To do this, you can simply draw a line over the numbers that x can be (so, for this example, x can be any number between 0 to 65).

Let me know if you have any questions!