Question #f6259

1 Answer
Nathan L.
Aug 14, 2017

#"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#.

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