Box one
9 in.
5.4 in.
Box two
3 in.
5 in.
What scale factor was used to enlarge the rectangle in the image? The measurements refer to inches. Give your answer as a decimal.
To find the scale factor, we need to compare the corresponding sides of the two boxes.
The vertical side of box one is 9 in, and the vertical side of box two is 3 in. So, the scale factor for the vertical side is 3/9 = 1/3.
The horizontal side of box one is 5.4 in, and the horizontal side of box two is 5 in. So, the scale factor for the horizontal side is 5/5.4 = 5/54.
Since both numbers are decimals (less than 1), we can simplify the fraction to its decimal form.
The scale factor for the vertical side is 1/3 = 0.3333 (rounded to four decimal places).
The scale factor for the horizontal side is 5/54 ≈ 0.0926 (rounded to four decimal places).
Therefore, the scale factor used to enlarge the rectangle in the image is approximately 0.3333 vertically and 0.0926 horizontally.
To find the scale factor used to enlarge the rectangle in the image, we need to compare the corresponding sides of the original and enlarged rectangles.
Let's start by comparing the lengths of the longer sides of the rectangles, which are 9 inches (Box one) and 5 inches (Box two). To find the scale factor, we divide the length of the longer side of the enlarged rectangle (Box two) by the length of the longer side of the original rectangle (Box one):
Scale factor = Length of the longer side of the enlarged rectangle / Length of the longer side of the original rectangle
Scale factor = 5 inches / 9 inches
Now, we can simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 1 in this case:
Scale factor = 5/9
Therefore, the scale factor used to enlarge the rectangle in the image is 5/9, which can also be expressed as a decimal: approximately 0.556 (rounded to three decimal places).
To determine the scale factor used to enlarge the rectangle in the image, we can compare the corresponding sides of the two rectangles.
For the width:
Original width: 9 in.
Enlarged width: 3 in.
So, the scale factor for the width is calculated as:
9 in. / 3 in. = 3
For the height:
Original height: 5.4 in.
Enlarged height: 5 in.
So, the scale factor for the height is calculated as:
5.4 in. / 5 in. = 1.08
Since the scale factor varies between the width and height, we take the average of these two scale factors to find the overall scale factor:
(3 + 1.08) / 2 = 2.04
Therefore, the scale factor used to enlarge the rectangle in the image is approximately 2.04.