Sabrina will construct a rectangle that has a height of 4
units and an area of up to 48
square units.

Which inequality represents all the possible lengths in units of the bases, b
, that Sabrina can use to construct this rectangle?
A.b≥52

B.b≤44

C.b≤12

D.b≥192

To solve this, we need to use the formula for the area of a rectangle:

\[
\text{Area} = \text{base} \times \text{height}
\]

Given:
- Height = 4 units
- Area ≤ 48 square units

Let \( b \) represent the length of the base. Then:

\[
b \times 4 \leq 48
\]

Dividing both sides by 4 to isolate \( b \):

\[
b \leq \frac{48}{4}
\]

\[
b \leq 12
\]

So, the inequality that represents all possible lengths \( b \) for the base is:

**C. \( b \leq 12 \)**

Would you like a further breakdown or explanation? 

Here are 5 additional questions that expand on this information:
1. What if the height was changed to 6 units but the area limit remained the same? How would this affect the possible base length?
2. How would you find possible base lengths if the area had to be exactly 48 square units instead?
3. If the base was 10 units, what would be the area of the rectangle?
4. How does changing the base impact the overall area if the height is fixed?
5. What are the possible values for the area if the base is set at 8 units?

**Tip:** When working with inequalities involving areas, dividing both sides by a positive number keeps the inequality direction the same.

Sabrina will construct a rectangle that has a height of 4 units and an area of up to 48 square units. Which inequality represents all the possible lengths in units of the bases, b, that Sabrina can use to construct this rectangle?

Explore how to solve inequalities for a rectangle with a height of 4 units and an area limit of 48 square units. Understand the steps to determine possible base lengths, using the area formula and inequality manipulation. This example is suitable for students in Grades 6-8 and provides foundational geometry and algebra skills.

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