Yuron is sketching a scale drawing of a famous painting. The painting is 54 inches wide and 72 inches long. He used a scale factor of 2/3 to make his sketch. How many inches wide is Yuron’s sketch?

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 \(\frac{2}{3}\) 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

\(S=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the corresponding side of the original figure}}.\)

Therefore, we have

\(\dfrac{2}{3}=\dfrac{\textup{width of Yuron's painting}}{\textup{width of the famous painting}}\\\\\\\Rightarrow \dfrac{2}{3}=\dfrac{w'}{w}\\\\\Rightarrow \dfrac{2}{3}=\dfrac{w'}{54}\\\\\\\Rightarrow w'=\dfrac{2\times 54}{3}\\\\\\\Rightarrow w'=36.\)

Thus, Yuron's painting is 36 inches wide.