Marie has a square piece of cloth. She needs another piece with a length 2 inches shorter than the side of the square piece and a width 2 inches longer. The area for the new piece of cloth is 780 in^2. What will be the dimensions of the new piece of cloth?
A: ?
(x-2)(x+2) = 780
x^2 - 4 = 780
x^2 = 784
Solve for x, then x+2 and x-2.
To find the dimensions of the new piece of cloth, we can use the information given in the question.
Let's say the side length of the square piece of cloth is "x" inches.
According to the question, the length of the new piece of cloth will be 2 inches shorter than the side of the square piece, so the length will be (x - 2) inches.
Similarly, the width of the new piece of cloth will be 2 inches longer than the side of the square piece, so the width will be (x + 2) inches.
We are also given that the area of the new piece of cloth is 780 in^2.
The formula for the area of a rectangle is length multiplied by width, so we can write:
Area = Length * Width
780 = (x - 2) * (x + 2)
Now, we can solve this equation to find the value of x, which will give us the side length of the square piece.
Expanding the equation:
780 = x^2 - 4
Rearranging the equation:
x^2 = 780 + 4
x^2 = 784
Taking the square root of both sides:
x = √784
x = 28
So, the side length of the square piece is 28 inches.
Now, we can find the dimensions of the new piece of cloth:
Length = x - 2 = 28 - 2 = 26 inches
Width = x + 2 = 28 + 2 = 30 inches
Therefore, the dimensions of the new piece of cloth are 26 inches by 30 inches.