A rectangular tablecloth is 2.5 m long. Trim is to be sewn around the perimeter of the cloth but there is not enough. What decrase in width will make the perimeter 0.4m shorter if the length remains the same?

Reduce the width by 0.2 m.

You would reduce the width by 0.2 m s

A community park wants to place a rectangular billboard to inform guests of their new attractions. Suppose the length of the billboard to be placed is 4m longer and its area is 96m2. What will be the dimensions?

To solve this problem, we can follow these steps:

Step 1: Identify the variables:
Let's assign variables to the given information:
Length of the tablecloth = 2.5 m
Decrease in width = x (unknown)
Decrease in perimeter (trim) = 0.4 m

Step 2: Determine the current dimensions:
We are given the length of the tablecloth, 2.5 m, but we need to find the width. Since there is not enough trim to go around the perimeter, we can assume the current width is greater than the current length.

Step 3: Use the perimeter formula:
The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (length + width)

Step 4: Calculate the initial perimeter:
Using the formula from Step 3, we can calculate the initial perimeter:
Initial Perimeter = 2 * (length + width)
Initial Perimeter = 2 * (2.5 + width)
Initial Perimeter = 5 + 2 * width

Step 5: Calculate the new perimeter:
Since the length remains the same, the new perimeter will be equal to the initial perimeter minus the decrease in perimeter:
New Perimeter = Initial Perimeter - Decrease in Perimeter
New Perimeter = 5 + 2 * width - 0.4

Step 6: Set up and solve the equation:
To find the decrease in width, we need to set up an equation by equating the new perimeter to the initial perimeter minus the decrease in perimeter:
New Perimeter = Initial Perimeter - Decrease in Perimeter
5 + 2 * width - 0.4 = 5 + 2 * (width - x)

Simplifying the equation:
5 + 2 * width - 0.4 = 5 + 2 * width - 2 * x

Cancellation:
2 * width and 2 * width cancel out:
5 - 0.4 = 5 - 2 * x

Simplifying:
4.6 = 5 - 2 * x

Step 7: Solve for x:
To find the decrease in width, we need to isolate the variable x:
4.6 = 5 - 2 * x
4.6 - 5 = -2 * x
-0.4 = -2 * x
-0.4 / -2 = x
0.2 = x

Step 8: Interpret the answer:
Therefore, a decrease in width by 0.2 m will make the perimeter 0.4 m shorter if the length remains the same.