To solve this problem you must apply the proccedure shown below:
1. You have that the dimensions of the picture in meters is:
[tex]5 cm=0.05m\\ 7cm=0.07m[/tex]
2. As you can see, the shorter side of the picture is [tex]0.05m[/tex].
3. Then, if the shorter side of the room is [tex]6m[/tex], you can find the scale of the picture by dividing the shorter side of the room by the shorter side of the picture, as following:
[tex]\frac{6m}{0.05m} =120[/tex] or [tex]1:120[/tex]
4. Then, you can calculate the longer side of the room by multiplying [tex]120[/tex] by the longer side of the picture:
[tex](0.07m)(120)=8.4m[/tex]
Therefore, the answer is: The scale of the picture is [tex]1:120[/tex] and the longer side of the room is [tex]8.4 m[/tex].
