Use an inequality to solve the problem. Be sure to show the inequality and all of your work.
The area of a triangle must be at most 32.5 square inches. The base is 13 inches and the height is x inches. Find the possible values for x.
To solve this problem, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
In this case, the base is given as 13 inches, and we want the area to be at most 32.5 square inches. Let's assume that the height is x inches.
We can set up an inequality to represent the relationship between the area, base, and height:
(1/2) * 13 * x ≤ 32.5
To solve this inequality, we can simplify it:
(13/2) * x ≤ 32.5
Next, we can multiply both sides of the inequality by 2/13 to isolate x:
x ≤ (32.5 * 2) / 13
x ≤ 5
Therefore, the possible values for x are any number less than or equal to 5 inches.