Answer:
Yes, it will fit
Step-by-step explanation:
The red part of the detail is [tex]4\dfrac{7}{9}\ cm[/tex] long, the yellow part is [tex]2\dfrac{1}{3}\ cm[/tex] long.
In order to fit the conditions, both parts together should be no longer than [tex]7\dfrac{1}{6}\ cm[/tex] and no less than [tex]7\dfrac{1}{18}\ cm.[/tex]
Find the combined length of red and yellow parts:
[tex]4\dfrac{7}{9}+2\dfrac{1}{3}\\ \\=(4+2)+\left(\dfrac{7}{9}+\dfrac{1}{3}\right)\\ \\=6+\left(\dfrac{7}{9}+\dfrac{3}{9}\right)\\ \\=6+\dfrac{10}{9}\\ \\=6+1\dfrac{1}{9}\\ \\=7\dfrac{1}{9}\ cm[/tex]
Note that
[tex]7\dfrac{1}{9}=7\dfrac{2}{18}>7\dfrac{1}{18},[/tex]
so the combined length is no less than [tex]7\dfrac{1}{18}\ cm[/tex]
and
[tex]7\dfrac{1}{9}=7\dfrac{2}{18}\\ \\7\dfrac{1}{6}=7\dfrac{3}{18}\\ \\7\dfrac{2}{18}<7\dfrac{3}{1}8\Rightarrow 7\dfrac{1}{9}<7\dfrac{1}{6},[/tex]
so the combined length is no more than [tex]7\dfrac{1}{6}\ cm[/tex]
