An algebraic expression for the perimeter of the picture frame is P = 3L.
- Let the length of the picture frame be L.
- Let the width of the picture frame be W.
- Let the perimeter of the picture frame be P.
Translating the word problem into an algebraic equation, we have;
The width of a picture frame is half ([tex]\frac{1}{2}[/tex]) the length:
[tex]W=\frac{L}{2}[/tex]
Formula for the perimeter of a rectangle.
Mathematically, the perimeter of a rectangle is given by the formula;
[tex]P=2(L+W)[/tex]
Where:
- P is the perimeter of a rectangle.
- L is the length of a rectangle.
- W is the width of a rectangle.
Substituting the parameters into the formula, we have;
[tex]P=2(L+\frac{L}{2})[/tex]
Simplifying further, we have:
[tex]P=2L+L\\\\[/tex]
P = 3L
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