A rectangular 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.

7*5=35

7 (2) + 5 (2) = 24

The dimensions are 7 and 5 inches.