The perimeter of a triangle is given by the following expression:
[tex]P=2\cdot(w+l)_{}[/tex]Where P is the perimeter, w is the width and l is the length.
We know that the ratio of the length to the width is 5 to 2. This means that for every 5 units of the length there are 2 units of the width, therefore:
[tex]5\cdot l=2\cdot w[/tex]If we isolate the "l" variable on the left, we have:
[tex]l=\frac{2\cdot w}{5}[/tex]We can replace the expression above on the formula for the perimeter.
[tex]P=2\cdot(\frac{2\cdot w}{5}+w)_{}[/tex]We now need to simplify the right side of the equation and isolate the "w" variable.
[tex]\begin{gathered} P=\frac{4w}{5}+2w \\ P=\frac{4w+10w}{5} \\ P=\frac{14w}{5} \\ w=\frac{5P}{14} \end{gathered}[/tex]The width is equal to 5/14 of the perimeter.
