Respuesta :
For this problem, we are given the perimeter of a rectangle and a relation between the width and the length. We need to determine the width.
The perimeter of a rectangle is given by:
[tex]P=2(\text{ width + length\rparen}[/tex]Therefore, we have:
[tex]2\text{ width}+2\text{ length}=64[/tex]We know that the width is 6 centimeters less than the length, therefore we can write the expression below:
[tex]\text{ width}=\text{ length}-6[/tex]If we replace the expression above on the second one, we have:
[tex]\begin{gathered} 2(\text{ length}-6)+2\text{ length}=64\\ \\ 2\text{ length}-12+2\text{ length}=64\\ \\ 4\text{ length}=64+12\\ \\ 4\text{ length}=76\\ \\ \text{ length}=\frac{76}{4}=19 \end{gathered}[/tex]We can use this value to find the width, which is:
[tex]\text{ width}=19-6=13[/tex]The width is equal to 13 cm.
