Respuesta :
The Solution:
Given:
The perimeter of a rectangle is 84.
We are asked to find the dimensions ( that is, length and width) of the rectangle.
Let the length of the rectangle be L and W for the width.
So,
[tex]L=2\frac{1}{2}of\text{ W}=\frac{5}{2}W[/tex]By formula, the perimeter of a rectangle is:
[tex]\begin{gathered} P=2(L+W) \\ \\ In\text{ this case,} \\ P=perimeter=84 \\ W=width=? \\ L=length=\frac{5}{2}W \end{gathered}[/tex]Substitute these values in the formula, we get:
[tex]84=2(\frac{5}{2}W+W)[/tex]Dividing both sides by 2, we get:
[tex]\begin{gathered} 42=\frac{5}{2}W+W \\ \\ 42=\frac{5W+2W}{2} \\ \\ 42=\frac{7W}{2} \end{gathered}[/tex]Cross multiplying, we get:
[tex]\begin{gathered} 7W=2\times42 \\ 7W=84 \end{gathered}[/tex]Dividing both sides by 7, we get:
[tex]W=\frac{84}{7}=12[/tex]To find the length L, we shall put 12 for W.
[tex]L=\frac{5}{2}W=\frac{5}{2}\times12=5\times6=30[/tex]Therefore, the dimensions of the rectangle is 30 by 12.
Length = 30 units
Width = 12 units
