### Home > MC2 > Chapter 10 > Lesson 10.1.3 > Problem10-34

10-34.

The art club has made a scale drawing of the new mural they will paint on the wall of the school. The area of the actual mural is $36$ times larger than the area of the drawing. What is the scale factor between the side length of the drawing and the side length of the mural?

Recall that area is always written in units$^{2}$ while side lengths are always written in units.
This means that the ratio of of the two areas is $36$ units$^{2}$.
To find the ratio of the sides, find the square root of the ratio of the two areas.

This is the ratio of the side lengths of the larger mural to that of the scale drawing. The scale factor is therefore $6$.
$\sqrt{\text{36 units^2}} = 6\text{ units}$