Question

The formula for the area of a rhombus is A = a equals StartFraction one-half EndFraction d 1 d 2.d1d2, where d1 and d2 are the lengths of the diagonals.
Which are equivalent equations? Select two correct answers.

d1 = 2Ad2
d1 = d 1 equals StartFraction 2 A Over d 2 EndFraction.
d2 = d 2 equals StartFraction d 1 Over d2 A EndFraction.
d2 = d 2 equals StartFraction 2 A Over d 1 EndFraction.
d2 = 2Ad1

Answer 1

Answer:

$\large\boxed{d_1=\dfrac{2A}{d_2};\ d_2=\dfrac{2A}{d_1}}$

Step-by-step explanation:

$A=\dfrac{1}{2}d_1d_2\qquad\text{multiply both sides by 2}\\\\2A=2\!\!\!\!\diagup\cdot\dfrac{1}{2\!\!\!\!\diagup}d_1d_2\\\\2A=d_1d_2\to d_1d_2=2A$

$\text{For}\ d_1:\\\\d_1d_2=2A\qquad\text{divide both sides by}\ d_2\neq0\\\\d_1=\dfrac{2A}{d_2}\\\\\text{For}\ d_2:\\\\d_1d_2=2A\qquad\text{divide both sides by}\ d_1\neq0\\\\d_2=\dfrac{2A}{d_1}$

Answer 2

Answer:

B and D

Step-by-step explanation: