Let "w" represent the width of the rectangular table and "l" represent the length.
You know that the length is 5 inches more than the width, you can express this as l=w+5
The perimeter of a rectangle can be calculated as twice the length plus twice the width
[tex]P=2l+2w[/tex]We know that P=78in and l=w+5, then:
[tex]78=2(w+5)+2w[/tex]From this expression, you can determine the width of the table:
- First, distribute the multiplication on the parentheses term:
[tex]\begin{gathered} 78=2\cdot w+2\cdot5+2w \\ 78=2w+10+2w \\ 78=4w+10 \end{gathered}[/tex]-Second, subtract 10 to both sides of the expression
[tex]\begin{gathered} 78-10=4w+10-10 \\ 68=4w \end{gathered}[/tex]-Third, divide both sides by 4
[tex]\begin{gathered} \frac{68}{4}=\frac{4}{4}w \\ 17=w \end{gathered}[/tex]The width of the table is 17inches.
Next, calculate the length
[tex]\begin{gathered} l=w+5 \\ l=17+5 \\ l=22 \end{gathered}[/tex]The length of the table is 22 inches.
