Final answer:
To find the values of x for which the area of the rectangle is larger than the perimeter, we can use the formulas for area and perimeter of a rectangle.
Step-by-step explanation:
To find the area and perimeter of the rectangle, we need to use the formulas:
Area = length * width
Perimeter = 2 * (length + width)
The length of the rectangle is given as 3x - 5, and the width is given as 10cm. We want to find the values of x for which the area is greater than the perimeter:
Area > Perimeter
Substituting the given values, we have:
(3x - 5) * 10 > 2 * ((3x - 5) + 10)
Expanding this equation, we get:
30x - 50 > 6x + 10
Combining like terms, we have:
24x > 60
Dividing both sides by 24, we get:
x > 2.5
Therefore, for values of x greater than 2.5, the area of the rectangle will be larger than the perimeter.