Question

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?

Answer 1

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
`(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=\frac{\textup{length of a side of the dilated figure}}{\textup{length of the corresponding side of the original figure}}.`

Therefore, we have

`(2)/(3)=\frac{\textup{width of Yuron's painting}}{\textup{width of the famous painting}}\\\\\\\Rightarrow (2)/(3)=(w')/(w)\\\\\Rightarrow (2)/(3)=(w')/(54)\\\\\\\Rightarrow w'=(2* 54)/(3)\\\\\\\Rightarrow w'=36.`

Thus, Yuron's painting is 36 inches wide.

Answer 2

54*(2/3)= 36= wide
72*(2/3)= 48= long