Arectangular table top has a perimeter of 24 inches and an area of 35 square inches. find its dimensions.

Hello : 
let : x  the lenght    y : the widith
the perimeter is ; 2(x+y)  and the area is : xy
so the system : 2(x+y) =24
                            xy  = 35  
  x+y = 12(1)
 xy = 35  ...(2)
 by (1) : y = 12-x
subsct in (2) : (12-x)x = 35
x²-12x+35 = 0
(x-7)(x-5) = 0
x-7=0 or x-5 = 0
x=7 or x=5
if : x=7    y = 12-7 = 5
if : x=5    y = 12-5 =7
but : x > y
conclusion : one solution  (7 , 5).

The dimensions are 7 and 5 inches.

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