Algebraic Expressions, Identities and Formulae - Forming Algebraic Expressions and Formulae

The formula for the perimeter \(P\) of a rectangle is given by:

\(P=2l+2w\)

where \(l\) is the length and \(w\) is the width.

1. Find the perimeter when \(l=8\) cm and \(w=5\) cm.
2. Make \(l\) the subject of the formula.
3. Given that the perimeter is \(30\) cm and the width is \(6\) cm, find the length.
4. The width is increased by \(3\) cm while the length remains the same.
   Write a new expression for the perimeter in terms of \(l\).

The formula for the area \(A\) of a rectangle is:

\(A=lw\)

5. Make \(w\) the subject of the formula.
6. If the area is \(48\) cm\(^2\) and the length is \(6\) cm, find the width.