Question

A rectangular table is six times as long as it is wide. If the area is `150` `ft^2`, what is the length and the width of the table?

Answer 1

The table is `5` feet wide and `30` feet long.

Explanation:

Let's call the width of the table `x`. We then know that the length is six times the width, so it is `6*x=6x`.

We know that the area of a rectangle is width times height, so the area of the table expressed in `x` will be:

`A=x*6x=6x^2`

We also knew that the area was `150` square feet, so we can set `6x^2` equal to `150` and solve the equation to get `x`:

`6x^2=150`

`(cancel6x^2)/cancel6=150/6`

`x^2=25`

`x=+-sqrt25=+-5`

Since lengths cannot be negative, we discard the negative solution, giving us that the width is equal to `5` feet. We knew the length was six times longer, so we just multiply `5` by `6` to get that the length is `30` feet.