Answer:
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
Answer: length = 6 cm; width = 5.5 cm
