Question

If the perimeter of the billiards table is 24 feet, what is the value of x?

Answer 1

Part A.

The width of the billiards table is: 4x-1

And the length is twice as long as the width. Given this information, the expression for the length is:

`2(4x-1)`

Use the distributive property to simplify the expression: multiply 2 times 4x, and 2 times -1:

`2\cdot4x-2\cdot1`

The simplified expression is:

`8x-2`

Part B.

We have the expression for the width and the length, this is represented for reference in the following diagram:

The rectangle represents the billiards table, and the shorter side is the width, and the longer side the length.

We can complete the sides of the billiards table by repeating the values on the opposite side:

And to calculate the perimeter we consider the following:

Thus, we get:

`4x-1+8x-2+4x-1+8x-2`

Combining like terms, we get the simplified algebraic expression for the perimeter of the table:

`24x-6`

Part C.

The perimeter of the table is equal to 24 feet, so we equal the last expression for the perimeter to 24:

`24x-6=24`

And solve for x by adding 6 to both sides of the expression:

`\begin{gathered} 24x-6+6=24+6 \\ 24x=30 \end{gathered}`

Divide both sides of the expression by 24:

`\begin{gathered} (24x)/(24)=(30)/(24) \\ x=1.25 \end{gathered}`

x is equal to 1.25 feet.