Respuesta :
Answer: Yuron's painting is 36 inches wide.
Step-by-step explanation: Given that Yuron is sketching a scale drawing of a famous painting which is 54 inches wide and 72 inches long. He used a scale factor of [tex]\frac{2}{3}[/tex] to make his sketch.
We are given to find the width Yuron’s sketch.
Let, w and w' represents the width of the famous painting and Yuron's painting.
Then, w = 54 inches, w' = ?
We know that the scale factor is defined by
[tex]S=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the corresponding side of the original figure}}.[/tex]
Therefore, we have
[tex]\dfrac{2}{3}=\dfrac{\textup{width of Yuron's painting}}{\textup{width of the famous painting}}\\\\\\\Rightarrow \dfrac{2}{3}=\dfrac{w'}{w}\\\\\Rightarrow \dfrac{2}{3}=\dfrac{w'}{54}\\\\\\\Rightarrow w'=\dfrac{2\times 54}{3}\\\\\\\Rightarrow w'=36.[/tex]
Thus, Yuron's painting is 36 inches wide.
