Sarah is making a scale drawing of a painting that is 48 in. wide by 120 in. high. Her paper is 12 in. wide and 24 in. tall. She decides to use the scale 1 in. = 4 in. Is this a reasonable scale?
Thank you!
The scale is 1 in= 4 in.
1:4= .25 or 25%
So 12/48= .25 or 25%
24/120= .2 or 20%
The ratio does not match the height ratio.
To determine if the chosen scale is reasonable, we need to compare the dimensions of the painting and the paper in both the actual size and the scale size.
1. Actual dimensions:
- The painting is 48 inches wide and 120 inches high.
- The paper is 12 inches wide and 24 inches tall.
2. Scale dimensions:
Since the chosen scale is 1 inch = 4 inches, we can calculate the scale dimensions by multiplying the actual dimensions by the scale factor (4).
- Scale width of the painting: 48 inches × 4 = 192 inches.
- Scale height of the painting: 120 inches × 4 = 480 inches.
Now, let's compare the scale dimensions with the size of the paper:
- Scale width of the painting (192 inches) is larger than the width of the paper (12 inches). This implies that the painting won't fit entirely on the paper when using the chosen scale.
- Scale height of the painting (480 inches) is also larger than the height of the paper (24 inches). Thus, the entire painting won't fit height-wise using this scale.
Based on this comparison, we can conclude that the chosen scale of 1 in. = 4 in. is not reasonable for Sarah's scale drawing because it would result in the painting being too large for her paper. She would need a larger piece of paper or a different scale to fit the entire painting.
since 48 = 4*12
and 120 = 5*24,
the 1:4 scale will work fine