Question

`A=(1)/(2)\pi w^2+2lw`

Solve for L

Answer 1

l = a/(2 w) - (π w)/4

Explanation:

Solve for l:

a = 2 l w + (π w^2)/2

a = 2 l w + (π w^2)/2 is equivalent to 2 l w + (π w^2)/2 = a:

2 l w + (π w^2)/2 = a

Subtract (π w^2)/2 from both sides:

2 l w = a - (π w^2)/2

Divide both sides by 2 w:

Answer: l = a/(2 w) - (π w)/4

Answer 2

`l=(2A-\pi w^2)/(4w)`

Explanation:

Subtract terms not containing L, then divide by its coefficient.

`A=(1)/(2)\pi w^2+2lw\\\\A-(1)/(2)\pi w^2=2lw\\\\l=(2A-\pi w^2)/(4w)`