Final answer:
The dimensions of the train ticket with an area of 153 square centimeters and a perimeter of 52 centimeters are 17 cm by 9 cm, satisfing the given area and perimeter conditions.
Step-by-step explanation:
The dimensions of the train ticket with an area of 153 square centimeters and a perimeter of 52 centimeters can be determined by setting up two equations based on the formulas for area (A = length × width) and perimeter (P = 2 × (length + width)). The ticket is rectangular, hence using the formulas:
- Area (A) = 153 cm² = length × width
- Perimeter (P) = 52 cm = 2 × (length + width)
To solve for length and width, we can divide the perimeter by 2 to find the sum of the length and width:
26 cm = length + width
Then subtract the width from both sides to find:
length = 26 cm - width
Now, substitute this expression for length into the area equation and solve for width. Once you have the width, you can plug it back into the perimeter equation to find the length. After solving the equations, the dimensions that satisfy both the area and perimeter are 17 cm by 9 cm (Option a).