Question

The perimeter of Henry's rectangular table is 78 inches. The length of the table is 5 inches more than the width. What is the length of the table?

Answer 1

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

`P=2l+2w`

We know that P=78in and l=w+5, then:

`78=2(w+5)+2w`

From this expression, you can determine the width of the table:

- First, distribute the multiplication on the parentheses term:

`\begin{gathered} 78=2\cdot w+2\cdot5+2w \\ 78=2w+10+2w \\ 78=4w+10 \end{gathered}`

-Second, subtract 10 to both sides of the expression

`\begin{gathered} 78-10=4w+10-10 \\ 68=4w \end{gathered}`

-Third, divide both sides by 4

`\begin{gathered} (68)/(4)=(4)/(4)w \\ 17=w \end{gathered}`

The width of the table is 17inches.

Next, calculate the length

`\begin{gathered} l=w+5 \\ l=17+5 \\ l=22 \end{gathered}`

The length of the table is 22 inches.