A train ticket has a perimeter of 62 centimeters and an area of 234 square centimeters. What are the dimensions of the ticket? centimeters by centimetersSubmit
Question
A train ticket has a perimeter of 62 centimeters and an area of 234 square centimeters. What are the dimensions of the ticket? centimeters by centimetersSubmit
Solution
The dimensions of the ticket can be found by solving the system of equations derived from the given information. The perimeter (P) of a rectangle is given by P = 2l + 2w, where l is the length and w is the width. The area (A) is given by A = lw.
From the problem, we know that P = 62 cm and A = 234 cm^2. This gives us the two equations:
2l + 2w = 62 lw = 234
We can simplify the first equation to l + w = 31.
To find the values of l and w, we can try different pairs of numbers that multiply to 234 and add up to 31.
The pair that works is 18 and 13.
18 * 13 = 234 18 + 13 = 31
So, the dimensions of the ticket are 18 centimeters by 13 centimeters.
Similar Questions
The perimeter of a rectangular painting is 332 centimeters. If the width of the painting is 73 centimeters, what is its length?centimeters
A rectangular building has an area of 1512 square metres. Its perimeter is 164 metres. What are the dimensions of the building?
A paper has an area of 624 square centimeters. What is the paper's area in square inches? Use the following conversion: 1 square inch is 6.5 square centimeters.
a rectangle which is three times a long as it is wide the same perimeter as a square of area 64cm^2. what is the length of the rectangle ?
The sides of a rectangle are in the ratio 5 : 7, and its perimeter is 96 cm. What is the area of the rectangle in square centimeters?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.