what do I do to solve this problem? I don't know how to work it out, so could somone show me to work it out. Please help!
the lenght of a rectangular playing field is 5 ft less than twice its width.the perimeter is 230 ft,so what is the lenght and width of the field.
Let L be the length and W be the width. According to your information, L = 2W - 5 (5 feet less than twice the width). The perimeter is 2L + 2W = 230. If L = 2W - 5, then substitute it into the perimeter equation. That is,
2(2W - 5) + 2W = 230 and solve. Using the information you get there, go back and solve for L. Don't forget to go back and check that your answers for W and L make sense.
The ratio of the lenght to width for a particular rectangle is 1.5. A scaled copy has width 6. What is the length of the scaled copy?
To solve this problem, follow these steps:
Step 1: Assign variables
Let's assign variables to the length and width of the field. We'll use L for the length and W for the width.
Step 2: Set up equations
Based on the information given, we know that the length L is 5 feet less than twice the width W. So we can write the equation: L = 2W - 5.
We also know that the perimeter of the field is 230 feet. The formula for the perimeter of a rectangle is P = 2L + 2W. So we can write the equation: 2L + 2W = 230.
Step 3: Substitute and simplify
Substitute the value of L from the first equation into the second equation. We get: 2(2W - 5) + 2W = 230.
Now, distribute the 2 to both terms inside the parentheses: 4W - 10 + 2W = 230.
Combine like terms: 6W - 10 = 230.
Step 4: Solve for W
To isolate the variable W, add 10 to both sides of the equation: 6W = 240.
Divide both sides of the equation by 6: W = 40.
Step 5: Solve for L
Now that we know W = 40, we can substitute this value into the first equation to solve for L: L = 2(40) - 5.
Simplify: L = 80 - 5 = 75.
Step 6: Check your answers
Make sure to go back and check if your answers for W and L make sense in the context of the problem.
The width of the field is 40 feet, and the length is 75 feet. To verify this, plug the values back into the equation for the perimeter: 2(75) + 2(40) = 230.
Simplify: 150 + 80 = 230.
The perimeter equation checks out, confirming that our values for W and L are correct.
Therefore, the length of the field is 75 feet, and the width is 40 feet.