Question

American Gothic is 29 7/8 inches high x 24 7/8 inches wide. If the canvas you are going to paint a proportional reproduction is 24 inches high, then what width (to the nearest tenth) should the canvas measure?

Answer 1

Answer on Question #48605 – Math – Geometry

American Gothic is 29 7/8 inches high x 24 7/8 inches wide. If the canvas you are going to paint a proportional reproduction is 24 inches high, then what width (to the nearest tenth) should the canvas measure?

Solution:

$$H = 29\frac{7}{8}$$

– height of the American Gothic;

$$W = 24\frac{7}{8}$$

– width of the American Gothic;

$$h = 24 \text{ inches}$$

– height of the canvas;

$$w = \text{width of the canvas}$$

The ratio $= \frac{\text{width}}{\text{height}}$ in first and in second case must be the same:

$$\frac{W}{H} = \frac{w}{h}$$

hence

$$w = \frac{W \cdot h}{H} = \frac{24\frac{7}{8} \cdot 24 \text{ inches}}{29\frac{7}{8}} = \frac{199 \cdot 24}{239} \approx 20 \text{ inches}$$

Answer: width of the canvas is 20 inches.

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