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: ?
If the old cloth had side s, the new cloth satisfies
(s-2)(s+2) = 780
26x30
To find the dimensions of the new piece of cloth, we need to use the information given and solve for the side length and width.
Let's say the side length of the square piece of cloth is x inches.
According to the given information, the length of the new piece of cloth is 2 inches shorter than the side length of the square piece. So, the length of the new piece will be (x - 2) inches.
Similarly, the width of the new piece is 2 inches longer than the side length of the square piece. So, the width of the new piece will be (x + 2) inches.
Now, we can calculate the area of the new piece using the formula: Area = Length * Width.
Given that the area of the new piece is 780 square inches, we can write the equation as:
780 = (x - 2) * (x + 2)
To solve this equation, we can expand it:
780 = x^2 - 4
Next, we can rearrange the equation to isolate x:
x^2 = 780 + 4
x^2 = 784
Taking the square root of both sides, we get:
x = √784
x = 28
Therefore, the side length of the square piece of cloth is 28 inches.
To find the dimensions of the new piece of cloth, we can substitute this value back into the formulas we found earlier:
Length = x - 2
Width = x + 2
Length = 28 - 2 = 26 inches
Width = 28 + 2 = 30 inches
So, the dimensions of the new piece of cloth will be 26 inches by 30 inches.