Question

Question #f6259

Answer 1

`"length" = 3x+2`

Explanation:

The equation for the perimeter of a rectangle is

`P = 2l + 2w`

where

• `l` is the length of the rectangle

• `w` is the width of the rectangle

We're given:

• `P = color(red)(8x-4`

• `w = color(green)(x-4`

Plugging these in:

`color(red)(8x-4) = 2l + 2(color(green)(x-4))`

Simplifying:

`8x-4 = 2l + 2x - 8`

Now we solve for `l`:

Subtract `2x` from both sides:

`6x - 4 = 2l - 8`

Add `8` to both sides:

`6x+4 = 2l`

Divide both sides by `2`:

`color(blue)(ulbar(|stackrel(" ")(" "l = 3x+2" ")|)`

The length of the rectangle (in terms of `x`) is thus `color(blue)(3x+2`.