What's with the shouting?

let the width be x

then the length is 2x - 6

now area is length times width, and we are told that is 108

=> length*width = 108

=> (2x - 6)x = 108

=> 2x^2 - 6x = 108

=> 2x^2 - 6x - 108 = 0

=> x^2 - 3x - 54 = 0

=> (x - 9)(x + 6) = 0

so x - 9 = 0 => x = 9

or x + 6 = 0 => x = -6

x cannot be -6, so x = 9

so the dimensions of the rectangle is: width = 9cm, length = 2x - 6 = 12cm

let the sides of the rectangle be x and y2. Find the dimensions of a rectangle whose perimeter is 46m and whose area is 126m^2 (squared).

let the perimeter be P

let the area be A

now P = 2x + 2y = 46

and A = xy = 126

so to find x and y, we need to solve the simultaneous equations:

2x + 2y = 46 ...................(1)

xy = 126 ........................(2)

x + y = 23 ..................(3) = (1)/2

xy = 126 .....................(2)

From (2), we see that x = 126/y, substitute 126/y for x in (3), we get:

126/y + y = 23

=> 126 + y^2 = 23y ...........i multiplied through by y

=> y^2 - 23y + 126 = 0

=> (y - 14)(y - 9) = 0

=> y - 14 = 0 => y = 14

or y - 9 = 0 => y = 9

but x + y = 23

=> x = 14 ...........when y = 9

or x = 9 .............when y = 14

x and y represent arbitrary sides, and the numbers are the same, so just pick one

so one side is 14 and the other is 9

you can say x = 14 and y = 9 or x = 9 and y = 14, same thing

this is exactly like the one above. why don't you try it and post your solution?3. Find the dimensions of a rectangle whose perimeter is 42m and whose area is 104^2 (squared).