# In the sketch, the height of Whisler's mother was 10 inches and the width of her gown was 8 1/3 inches. In the actual painting, the height of his mother was 50 inches. How would I find the width of her gown?

Apr 4, 2015

The answer is: $41 \frac{2}{3}$

If his mother's height was $5$ times longer than the sketch, then the width of her gown should be $5$ times wider too.

Lets say the width of the gown is $k$ inches.

Everything should be scaled with the same proportions so:

$\frac{10}{50} = \frac{8 + \frac{1}{3}}{k}$

$\frac{1}{5} = \frac{8 + \frac{1}{3}}{k}$

$k = 5 \cdot \left(8 + \frac{1}{3}\right) = 40 + \frac{5}{3} = 40 + \left(1 + \frac{2}{3}\right)$

$k = 41 + \frac{2}{3}$ inches