Question
Gus is knitting a scarf in the shape of a parallelogram. The height of the parallelogram will be 25 cm. He only has enough yarn to knit a maximum area of 1,000 cm^2. How would you write an inequality to express the possible length of the base, b, of the parallelogram?
1,000___25b
1,000___25b
Answers
GPT-4o mini
To express the maximum area of a parallelogram, we can use the formula for the area, which is given by:
\[
\text{Area} = \text{base} \times \text{height}
\]
In this case, the area must be less than or equal to 1,000 cm², and the height is given as 25 cm. Therefore, we can set up the inequality based on the area:
\[
\text{Area} \leq 1,000 \quad \Rightarrow \quad b \times 25 \leq 1,000
\]
To express this in terms of \(b\), we can divide both sides of the inequality by 25:
\[
b \leq \frac{1,000}{25}
\]
Calculating \(\frac{1,000}{25}\):
\[
\frac{1,000}{25} = 40
\]
Thus, we can express the length of the base \(b\) with the inequality:
\[
b \leq 40
\]
So the complete inequality describing the possible lengths for \(b\) is:
\[
b \leq 40
\]
In the form as requested, it can be written as:
\[
1,000 \geq 25b
\]
or equivalently, rearranged as:
\[
25b \leq 1,000
\]
\[
\text{Area} = \text{base} \times \text{height}
\]
In this case, the area must be less than or equal to 1,000 cm², and the height is given as 25 cm. Therefore, we can set up the inequality based on the area:
\[
\text{Area} \leq 1,000 \quad \Rightarrow \quad b \times 25 \leq 1,000
\]
To express this in terms of \(b\), we can divide both sides of the inequality by 25:
\[
b \leq \frac{1,000}{25}
\]
Calculating \(\frac{1,000}{25}\):
\[
\frac{1,000}{25} = 40
\]
Thus, we can express the length of the base \(b\) with the inequality:
\[
b \leq 40
\]
So the complete inequality describing the possible lengths for \(b\) is:
\[
b \leq 40
\]
In the form as requested, it can be written as:
\[
1,000 \geq 25b
\]
or equivalently, rearranged as:
\[
25b \leq 1,000
\]