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?

Lyla Carson 2022-09-23 Answered
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 1 4 but no idea how.
Any ideas how to solve it?
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Answers (1)

panterafan101wx
Answered 2022-09-24 Author has 6 answers
Well, for any rectangle, the perimeter is given by
P = 2 L + 2 W
where L and W are the lengths and widths. Plugging in the values you get, we get
P = 2 ( 5 x + 1 ) + 2 ( 2 x ) = 10 x + 1 + 4 x = 14 x + 4 x ( x + 1 )
Since the perimeter is given as 20, then
24 = 14 x + 4 x ( x + 1 )
24 x ( x + 1 ) = 14 x + 4
24 x 2 + 24 x = 14 x + 4
24 x 2 + 10 x 4 = 0
12 x 2 + 5 x 2 = 0
x = 5 ± 11 20 = 1 4 , 2 3
Since x can't be negative, or else we'd have negative side lengths, the correct answer is given as
x = 1 4
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