A rectangle is 9 inches wide and 5.4 inches tall and a square is 5 inches wide and 3 inches tall
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 used to enlarge the rectangle, we can compare the corresponding side lengths of the original and enlarged rectangle.
The original rectangle has a width of 9 inches. Let's say the enlarged rectangle has a width of W inches.
The original rectangle has a height of 5.4 inches. Let's say the enlarged rectangle has a height of H inches.
If we divide the width of the enlarged rectangle by the width of the original rectangle, we should get the same ratio when we divide the height of the enlarged rectangle by the height of the original rectangle.
W/9 = H/5.4
Simplifying this equation, we can cross-multiply:
5.4W = 9H
Dividing both sides by 5.4 to isolate W, we get:
W = (9H)/5.4
We are given that the square has a width of 5 inches and a height of 3 inches. Let's substitute these values into the equation above.
W = (9*3)/5.4 = 27/5.4 = 5
So the width of the enlarged rectangle is 5 inches.
To find the scale factor, we need to divide the width of the enlarged rectangle by the width of the original rectangle:
Scale factor = 5/9 ≈ 0.5556
Therefore, the scale factor used to enlarge the rectangle is approximately 0.5556.