Oceanographers use a quantity known as shoreline development to
describe and categorize bodies of water. Shoreline development, D,
measures how closely a body of water resembles a circle. Its formula is:
where L is the shoreline length and A is the area of the body of water. Solve this formula for A.
Cannot see the formula. You can solve for A by using the same rules you use to solve equations with numbers.
To solve the formula D = (pi * L) / (2 * sqrt(pi * A)), we need to isolate the variable A.
Here are the steps to solve for A:
1. Multiply both sides of the equation by (2 * sqrt(pi * A)) to get rid of the denominator:
D * (2 * sqrt(pi * A)) = pi * L
2. Divide both sides of the equation by D to isolate the term with A:
(2 * sqrt(pi * A)) = (pi * L) / D
3. Divide both sides of the equation by 2 to simplify:
sqrt(pi * A) = (pi * L) / (2 * D)
4. Square both sides of the equation to eliminate the square root:
pi * A = ((pi * L) / (2 * D)) ^ 2
5. Divide both sides of the equation by pi to solve for A:
A = (((pi * L) / (2 * D)) ^ 2) / pi
Therefore, the formula for A in terms of D and L is:
A = (((pi * L) / (2 * D)) ^ 2) / pi