Let's start by solving the given equation for $d_1$.

The equation is:

$A = \frac{d_1 \cdot d_2}{2}$

To solve for $d_1$, follow these steps:

1. Multiply both sides of the equation by 2 to eliminate the denominator:

$2A = d_1 \cdot d_2$

2. Divide both sides by $d_2$ to isolate $d_1$:

$d_1 = \frac{2A}{d_2}$

Now that we have the solution $d_1 = \frac{2A}{d_2}$, let's examine the provided choices.

• Choice 1: $d_1 = \frac{2A}{d_2}$ – This is correct.
• Choice 2: $d_1 = \frac{2A}{d_2}$ – This is a duplicate of Choice 1, so it is also correct.
• Choice 3: $d_1 = \frac{2d_2}{A}$ – This is incorrect. The correct formula has $d_2$ in the denominator, not the numerator.
• Choice 4: $d_1 = \frac{A \cdot d_2}{2}$ – This is incorrect. The formula should have 2 in the numerator, not the denominator.
• Choice 5: $d_1 = \frac{A}{2d_2}$ – This is incorrect. It does not match the correct formula.

Correct answers:

• $d_1 = \frac{2A}{d_2}$ (Choice 1 and Choice 2)

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Would you like further details on this solution or have any questions?

Here are five related questions to expand your understanding:

1. How would the equation change if the formula was $A = d_1 \cdot d_2$?
2. Can you derive $d_2$ from the original equation in terms of $A$ and $d_1$?
3. What happens if $d_2 = 0$? How does it affect the equation?
4. What is the significance of multiplying both sides of an equation by a number?
5. How can you verify that $d_1 = \frac{2A}{d_2}$ is the correct solution?

Tip: Always check for extraneous solutions by substituting the values back into the original equation to ensure they satisfy the equation.