9 in.
5.4 in.
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 original rectangle and the enlarged rectangle.
For the width:
Original width = 5.4 in.
Enlarged width = 9 in.
Scale factor for the width = Enlarged width / Original width = 9 / 5.4 = 1.6667
For the height:
Original height = 3 in.
Enlarged height = 5 in.
Scale factor for the height = Enlarged height / Original height = 5 / 3 = 1.6667
Since both the scale factors for the width and height are the same, we can conclude that the overall scale factor used to enlarge the rectangle in the image is 1.6667.
To find the scale factor used to enlarge the rectangle in the image, we need to compare corresponding measurements before and after the enlargement.
Let's take the length as an example:
Before enlargement:
Length = 9 inches
After enlargement:
Length = 5.4 inches
To find the scale factor, we can divide the length after enlargement by the length before enlargement:
Scale factor = Length after enlargement / Length before enlargement
Scale factor = 5.4 inches / 9 inches
Simplifying this ratio, we get:
Scale factor = 0.6
Therefore, the scale factor used to enlarge the rectangle in the image is 0.6 (as a decimal).
To determine the scale factor used to enlarge the rectangle in the image, we need to compare the corresponding sides of the original and enlarged rectangle.
Let's denote the original measurements as follows:
Original rectangle:
Length: L1 = 9 in
Width: W1 = 5.4 in
Enlarged rectangle:
Length: L2
Width: W2
To find the scale factor, we can use the ratio of the corresponding side lengths:
Scale factor = L2 / L1 = W2 / W1
Let's plug in the values:
Scale factor = L2 / 9 in = W2 / 5.4 in
Now, let's calculate the scale factor by finding the value of L2:
L2 = (Scale factor) * L1 = (Scale factor) * 9 in
Our goal is to find the value of the scale factor.
Similarly, let's calculate the value of W2:
W2 = (Scale factor) * W1 = (Scale factor) * 5.4 in
Now, we have two equations:
Scale factor = L2 / 9 in
Scale factor = W2 / 5.4 in
Since both equations are equal to the scale factor, we can set them equal to each other:
L2 / 9 in = W2 / 5.4 in
Let's cross-multiply and solve for L2:
L2 * 5.4 in = 9 in * W2
L2 = (9 in * W2) / 5.4 in
Now, we can substitute this value of L2 in the previous equation to solve for the scale factor:
(9 in * W2) / 5.4 in = W2 / 5.4 in
Cross-multiply:
9 in * W2 = W2 * 5.4 in
Divide both sides by W2:
9 in = 5.4 in
Now, we can solve for the value of W2:
W2 = 5.4 in * 5 / 9
W2 = 30 in / 9
W2 ≈ 3.333 in
Finally, we can substitute this value of W2 back into the equation for the scale factor:
Scale factor = L2 / 9 in = 3.333 in / 9 in
Scale factor ≈ 0.3704
Therefore, the scale factor used to enlarge the rectangle in the image is approximately 0.3704 (as a decimal).