# Using Algebraic Fractions To Find Perimeter Make a formula to find the perimeter of the rectangle, the perimeter is 24 units. The longer side is 5/(x+1) and the shorter side is 2/x.I know that the answer is 14 but no idea how.Any ideas how to solve it?

Using Algebraic Fractions To Find Perimeter
Make a formula to find the perimeter of the rectangle, the perimeter is 24 units.
The longer side is $\frac{5}{x+1}$ and the shorter side is $\frac{2}{x}$
I know that the answer is $\frac{1}{4}$ but no idea how.
Any ideas how to solve it?
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panterafan101wx
Well, for any rectangle, the perimeter is given by
$P=2L+2W$
where $L$ and $W$ are the lengths and widths. Plugging in the values you get, we get
$P=2\left(\frac{5}{x+1}\right)+2\left(\frac{2}{x}\right)=\frac{10}{x+1}+\frac{4}{x}=\frac{14x+4}{x\left(x+1\right)}$
Since the perimeter is given as $20$, then
$24=\frac{14x+4}{x\left(x+1\right)}$
$24x\left(x+1\right)=14x+4$
$24{x}^{2}+24x=14x+4$
$24{x}^{2}+10x-4=0$
$12{x}^{2}+5x-2=0$
$x=\frac{-5±11}{20}=\frac{1}{4},-\frac{2}{3}$
Since $x$ can't be negative, or else we'd have negative side lengths, the correct answer is given as
$x=\frac{1}{4}$