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

The answer is B and D.

Explanation:

Edge 2020

Answer 2

`\large\boxed{d_1=(2A)/(d_2);\ d_2=(2A)/(d_1)}`

Explanation:

`A=(1)/(2)d_1d_2\qquad\text{multiply both sides by 2}\\\\2A=2\!\!\!\!\diagup\cdot(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\\eq0\\\\d_1=(2A)/(d_2)\\\\\text{For}\ d_2:\\\\d_1d_2=2A\qquad\text{divide both sides by}\ d_1\\eq0\\\\d_2=(2A)/(d_1)`