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.
