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The area \( A \) of a rhombus is given by the formula \( A = \frac{1}{2} d_1 d_2 \) where \( d_1 \) and \( d_2 \) are the lengths of the diagonals. Which equation could you use to find the value of \( d_1 \) for different values of \( d_2 \) and \( A \)?

A. \( d_1 = A \left(\frac{d_2}{2}\right) \)

B. \( d_1 = \frac{2A}{d_2} \)

C. \( d_1 = \frac{A}{2d_2} \)

D. [tex]\( d_1 = A - d_2 - \frac{1}{2} \)[/tex]

Sagot :

GinnyAnsweridn
To find the value of \( d_1 \) for different values of \( d_2 \) and \( A \), we start with the given formula for the area of a rhombus:

[tex]\[ A = \frac{1}{2} d_1 d_2 \][/tex]

We need to rearrange this equation to solve for \( d_1 \). First, let's isolate \( d_1 \) on one side of the equation.

1. Start with the area formula:
[tex]\[ A = \frac{1}{2} d_1 d_2 \][/tex]

2. Multiply both sides of the equation by 2 to get rid of the fraction:
[tex]\[ 2A = d_1 d_2 \][/tex]

3. Now, divide both sides by \( d_2 \) to solve for \( d_1 \):
[tex]\[ d_1 = \frac{2A}{d_2} \][/tex]

Therefore, the equation to find \( d_1 \) when \( d_2 \) and \( A \) are given is:

[tex]\[ d_1 = \frac{2A}{d_2} \][/tex]

Hence, the correct choice is:

[tex]\[ \boxed{B} \][/tex]