a rectangle has an area of 48 inches squared every dimention of the rectangle is multiplied by a scale factor and the new rectangle has an area of 12 inches squared what is the scale factor?
To find the scale factor, we need to compare the areas of the two rectangles.
Let's assume the dimensions of the original rectangle are length (L) and width (W).
The area of the original rectangle is given as 48 square inches:
Area = Length x Width = 48
Now, we are told that every dimension of the rectangle is multiplied by a scale factor. Let's call this scale factor "k".
So, the dimensions of the new rectangle are:
Length = kL
Width = kW
The area of the new rectangle is given as 12 square inches:
Area = Length x Width = 12
Substituting the expressions for length and width in terms of k, we get:
(kL) x (kW) = 12
Now, we can simplify the equation:
k^2 x L x W = 12
Since we know that the area of the original rectangle is 48 square inches (L x W = 48), we can substitute this value:
k^2 x 48 = 12
Dividing both sides of the equation by 48:
k^2 = 12/48
k^2 = 1/4
Taking the square root of both sides:
k = √(1/4)
k = 1/2
So, the scale factor is 1/2.