Question
The base of a parallelogram is 0.7 m the area must be no more than 0.63 m how would you write an inequality to show the possible heights of the parallelogram A 0.7 underline > 0.63h B 0.63 underline > 0.7h C 0.7 > 0.63h D 0.63 > 0.7h
Answers
Answered by
GPT-4o mini
To find the relationship between the base, height, and area of a parallelogram, you can use the formula for the area:
\[
\text{Area} = \text{base} \times \text{height}
\]
In your case, the base of the parallelogram is \(0.7\) m, and the area must be no more than \(0.63\) m². Therefore, we can set up the inequality as follows:
\[
0.7 \times h \leq 0.63
\]
To isolate \(h\), divide both sides by \(0.7\):
\[
h \leq \frac{0.63}{0.7}
\]
This means that the height \(h\) must be less than or equal to \(\frac{0.63}{0.7}\) (approximately \(0.9\)).
When looking at the options you provided, we can rewrite the inequality \(0.7h \leq 0.63\) in the form involving the area:
1. Rearranging gives us \(0.63 \geq 0.7h\).
This indicates the option **A** as the correct inequality does not fit, and actually, we can identify the right expression from the context of others provided:
**Answer:** The closest representation in standard format would have to be **\(0.63 \geq 0.7h\)**, which is akin to B's context, if one reflects on an upper boundary interpretation (however more correctly with strict association to height less than rather than equal simplistic formulation itself given height interpretations).
In summary, the right interpretation has the area reflecting over base used.
\[
\text{Area} = \text{base} \times \text{height}
\]
In your case, the base of the parallelogram is \(0.7\) m, and the area must be no more than \(0.63\) m². Therefore, we can set up the inequality as follows:
\[
0.7 \times h \leq 0.63
\]
To isolate \(h\), divide both sides by \(0.7\):
\[
h \leq \frac{0.63}{0.7}
\]
This means that the height \(h\) must be less than or equal to \(\frac{0.63}{0.7}\) (approximately \(0.9\)).
When looking at the options you provided, we can rewrite the inequality \(0.7h \leq 0.63\) in the form involving the area:
1. Rearranging gives us \(0.63 \geq 0.7h\).
This indicates the option **A** as the correct inequality does not fit, and actually, we can identify the right expression from the context of others provided:
**Answer:** The closest representation in standard format would have to be **\(0.63 \geq 0.7h\)**, which is akin to B's context, if one reflects on an upper boundary interpretation (however more correctly with strict association to height less than rather than equal simplistic formulation itself given height interpretations).
In summary, the right interpretation has the area reflecting over base used.