Question 9

Explanation

We will determine the set of values for $x$ that satisfies the condition for the cuboid to have real (positive) dimensions.

Determining Cuboid Dimensions

Based on the previous question and the given information:

• Length ($p$) = $5 - x$
• Width ($l$) = $4x - 5$
• Height ($t$) = $5 - \frac{1}{3}x$

Positive Dimension Conditions

For the cuboid to be real, all its dimensions must be positive ($> 0$).

Condition 1: $p > 0$

Condition 2: $l > 0$

Condition 3: $t > 0$

Determining Set Intersection

We find the intersection of these three conditions:

1. $x < 5$
2. $x > \frac{5}{4}$ (or $1.25$)
3. $x < 15$

From conditions 1 and 3, we take the stricter one, which is $x < 5$. Combined with condition 2, we get the range:

So, the set $A$ is: