(2{x}^{-3}{y}^{5})(-{4}^{8}{y}^{2})(2x −3
y
5
)(−4
8
y
2
)

length = 6 cm; width = 5.5 cm

Step-by-step explanation:

Let the length = x. Let the width = y.

We use the formulas for area and perimeter using x and y, and the given values.

area = length * width

perimeter = 2(length + width)

xy = 33

2(x + y) = 23

Solve the first equation for x:

x = 33/y

Substitute 33/y for x in the second equation.

2(33/y + y) = 23

66/y + 2y = 23

Mulrtiply both sides by y.

66 + 2y^2 = 23y

2y^2 - 23y + 66 = 0

(2y - 11)(y - 6) = 0

2y - 11 = 0   or   y - 6 = 0

y = 11/2 = 5.5   or   y = 6

xy = 33

x * 11/2 = 33

x = 33 * 2/11

x = 6

length = 6 cm; width = 5.5 cm