Question

solve the literal equation.

1. solve (z - m=at) for (z).
2. solve (mn + f=ab) for (n).
3. the perimeter (p) of a rectangle is given by the formula (p = 2l+2w) where (l) is the length and (w) is the width.

a) solve the formula for the length (l).
b) then use the rewritten formula to find the length of the rectangle with a width of (5ft) and a perimeter of (50ft).

Explanation:

Step1: Isolate the term with \(l\)

Subtract \(2w\) from both sides of \(P = 2l+2w\): \(P - 2w=2l\).

Step2: Solve for \(l\)

Divide both sides by 2: \(l=\frac{P - 2w}{2}\).

for part b:

Step1: Substitute values

Substitute \(P = 50\) and \(w = 5\) into \(l=\frac{P - 2w}{2}\). So \(l=\frac{50-2\times5}{2}\).

Step2: Simplify

First, calculate the numerator: \(50-2\times5=50 - 10=40\). Then, \(\frac{40}{2}=20\).

Answer:

for part a:
\(l=\frac{P - 2w}{2}\)