If the rectangles width is trippled and its length is doubled the perimeter of the new rectangle is 92 centimeter greater than the original perimeter what is the area of the original rectangle?
original perimeter = 2L + 2w
new length = 2L
new width = 3W
new perimeter = 4L + 6w
4L+6w - (2L+2w) = 92
2L + 4w = 92
L + 2w = 46
L = 46-2w
area of original = lw
= w(46-2w)
= 46w - 2w^2
To solve this problem, we can start by setting up some equations based on the given information. Let's denote the original width and length of the rectangle as 'w' and 'l' respectively.
According to the problem, if the width is tripled, the new width becomes 3w. Similarly, if the length is doubled, the new length becomes 2l.
Now, let's calculate the perimeters of the original and new rectangles. The perimeter is given by the formula: 2 * (length + width).
For the original rectangle, the perimeter is: 2 * (l + w).
For the new rectangle, the perimeter is: 2 * (2l + 3w).
The problem states that the new perimeter is 92 centimeters greater than the original perimeter. So we can write the following equation:
2 * (2l + 3w) = 2 * (l + w) + 92
Now let's simplify this equation:
4l + 6w = 2l + 2w + 92
Combining like terms:
4l - 2l + 6w - 2w = 92
2l + 4w = 92
Now we have a linear equation with two variables. We can solve it to find the values of 'l' and 'w'.
However, in order to calculate the area of the original rectangle, we need to know both the width and length. Without that information, it is not possible to calculate the area of the original rectangle.