The rectangle given has a perimeter of 14 units. Find the value(s) of x by factoring a quadriatic equation.

Question

one side= 12/(x+1)
other side= 6/(4-x)

Remember that the perimeter of a rectangle is: P = 2L + 2W

Note: P = perimeter, L = length, and W = width.

Therefore:

14 = 2[12/(x+1)] + 2[6/(4-x)]

14 = 24/(x+1) + 12/(4-x)

Common denominator is (x+1)(4-x).

14 = 24(4-x)/(x+1)(4-x) + 12(x+1)/(x+1)(4-x)

14 = {[24(4-x)] + [12(x+1)]}/(x+1)(4-x)

14 = (96 - 24x + 12x + 12)/(x+1)(4-x)

14 = (108 - 12x)/(x+1)(4-x)

Multiplying both sides by (x+1)(4-x) we have this result:

14(x+1)(4-x) = 108 - 12x

-14(x+1)(x-4) = 108 - 12x

-14(x^2 - 4x + x - 4) = 108 - 12x

-14(x^2 - 3x - 4) = 108 - 12x

-14x^2 + 42x + 56 = 108 - 12x

Set the equation equal to 0:

-14x^2 + 42x + 56 - 108 + 12x = 0

-14x^2 + 54x - 52 = 0

Factor out -2:

-2(7x^2 - 27x + 26) = 0

Then factor 7x^2 - 27x + 26:

-2(7x - 13)(x - 2) = 0

Set each factor in the parentheses equal to 0:

7x - 13 = 0; x = 13/7
x - 2 = 0; x = 2

Check these values with the original equation. It always helps to check your work!

I hope this will help with other problems of this type.

thank you soo much for all your help. I was just wondering if you can give me an outline of what steps to do for next time. such as:
find CD.
times both sides by CD.

thanks again.
Shay.