To find the equivalent equations to the given area formula for a rhombus, [tex]\(A = \frac{1}{2} d_1 d_2\)[/tex], we need to rearrange the formula to solve for both [tex]\(d_1\)[/tex] and [tex]\(d_2\)[/tex].
1. Start with the original formula:
[tex]\[
A = \frac{1}{2} d_1 d_2
\][/tex]
2. Solving for [tex]\(d_1\)[/tex]:
- Multiply both sides by 2 to clear the fraction:
[tex]\[
2A = d_1 d_2
\][/tex]
- Divide both sides by [tex]\(d_2\)[/tex] to solve for [tex]\(d_1\)[/tex]:
[tex]\[
d_1 = \frac{2A}{d_2}
\][/tex]
3. Solving for [tex]\(d_2\)[/tex]:
- Again, start with:
[tex]\[
2A = d_1 d_2
\][/tex]
- Divide both sides by [tex]\(d_1\)[/tex] to solve for [tex]\(d_2\)[/tex]:
[tex]\[
d_2 = \frac{2A}{d_1}
\][/tex]
The equivalent equations are:
1. [tex]\(d_1 = \frac{2A}{d_2}\)[/tex]
2. [tex]\(d_2 = \frac{2A}{d_1}\)[/tex]
Based on these, the correct selections from the provided options are:
- [tex]\(d_1 = \frac{2 A}{d_2}\)[/tex]
- [tex]\(d_2 = \frac{2 A}{d_1}\)[/tex]
Therefore, the correct answers are:
[tex]\[
d_1 = \frac{2 A}{d_2}, \quad d_2 = \frac{2 A}{d_1}
\][/tex]
