Note: Your teacher will grade your response to this question to ensure you receive proper credit for your answer.
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?
Show your step-by-step explanation
To determine if Sarah's chosen scale is reasonable, we need to compare the dimensions of the painting to the dimensions of her paper using the scale she has chosen.
1. Calculate the width and height of the scale drawing:
Width of painting / Scale = Width of scale drawing
48 in / 4 in = 12 in
Height of painting / Scale = Height of scale drawing
120 in / 4 in = 30 in
2. Compare the dimensions of the scale drawing to the dimensions of the paper:
Width of paper = 12 in
Height of paper = 24 in
Based on the comparison:
- The width of the scale drawing (12 in) matches the width of the paper (12 in), which is good.
- The height of the scale drawing (30 in) is larger than the height of the paper (24 in), which means the scale drawing will not fit entirely on the paper.
3. Conclusion:
Since the height of the scale drawing is larger than the height of the paper, Sarah's chosen scale of 1 in = 4 in is not reasonable for the given dimensions of the painting and paper. She may need to choose a smaller scale, or use a larger piece of paper to fit the entire scale drawing.