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 cm2
. How would you write an inequality to express the possible length of the base, b
, of the parallelogram? You will find the option to add inequality symbols in the Comparison (<)
keyboard.(1 point)
1,000 ____ 25b
. How would you write an inequality to express the possible length of the base, b
, of the parallelogram? You will find the option to add inequality symbols in the Comparison (<)
keyboard.(1 point)
1,000 ____ 25b
Answers
GPT-4o mini
To express the area of a parallelogram, you can use the formula:
\[ \text{Area} = \text{base} \times \text{height} \]
In this case, the area is represented by \( A = b \times h \), where \( b \) is the base and \( h \) is the height. For Gus's scarf, the height \( h \) is 25 cm and the maximum area \( A \) is 1,000 cm².
So, you can write the inequality based on the formula:
\[ b \times 25 \leq 1000 \]
To isolate \( b \), divide both sides by 25:
\[ b \leq \frac{1000}{25} \]
Calculating the right side gives:
\[ b \leq 40 \]
Therefore, you can express this in the context of your question as:
\[ 1,000 \geq 25b \]
So the correct inequality to fill in the blank is:
**1,000 ≥ 25b**
\[ \text{Area} = \text{base} \times \text{height} \]
In this case, the area is represented by \( A = b \times h \), where \( b \) is the base and \( h \) is the height. For Gus's scarf, the height \( h \) is 25 cm and the maximum area \( A \) is 1,000 cm².
So, you can write the inequality based on the formula:
\[ b \times 25 \leq 1000 \]
To isolate \( b \), divide both sides by 25:
\[ b \leq \frac{1000}{25} \]
Calculating the right side gives:
\[ b \leq 40 \]
Therefore, you can express this in the context of your question as:
\[ 1,000 \geq 25b \]
So the correct inequality to fill in the blank is:
**1,000 ≥ 25b**