We have a picture frame with width being 3 1/4 inches and length unknown. We need to fit picture with width of 4 cm and length 4.6 cm into frame.
What is the scale factor for enlargement?
What is length of unknown side of frame?
I was given the answer as the scale factor being 2.08 but have no idea how this number was found. Please help to explain! Thank you
the ratio of 3.25in : 4cm for the short side is
3.25*2.54/4 = 2.07
close enough for jazz.
Now use that scale factor to enlarge 4.6cm. Probably should express the answer in inches, as well, since that was the original frame size unit.
Actually, you don't need the scale factor at all. 4.6 is 1.15 times as big as 4, so the length will be
3.25 * 1.15 = 3.7375 inches
That's an unusual number, so a more common length would be 3 3/4, or 3.75 inches
To find the scale factor for enlargement, we need to compare the original dimensions of the picture with the dimensions of the picture when it is enlarged to fit the frame.
The original width of the picture is given as 4 cm, and the width of the frame is given as 3 1/4 inches. Since we want to compare these measurements, we need to convert the width of the frame to the same unit as the width of the picture.
To convert 3 1/4 inches to centimeters, we can use the conversion factor of 2.54 cm per inch.
3 1/4 inches = 3.25 inches
3.25 inches * 2.54 cm/inch ≈ 8.255 cm
So, the original width of the picture is 4 cm, and the width of the frame is approximately 8.255 cm.
Now, we can calculate the scale factor for enlargement by dividing the width of the frame by the width of the picture:
Scale Factor = Width of Frame / Width of Picture
Scale Factor = 8.255 cm / 4 cm
Scale Factor ≈ 2.064
Therefore, the scale factor for enlargement is approximately 2.064.
To find the length of the unknown side of the frame, we can use the same scale factor.
The original length of the picture is given as 4.6 cm. We can now find the length of the unknown side of the frame by multiplying the original length of the picture by the scale factor:
Length of Frame = Length of Picture * Scale Factor
Length of Frame = 4.6 cm * 2.064
Length of Frame ≈ 9.5184 cm
Therefore, the length of the unknown side of the frame is approximately 9.5184 cm.