Answer:
6 inches
Step-by-step explanation:
To solve this problem, we first need to find the perimeter of the larger rectangle. The formula for a perimeter is: [tex]2(l+w)[/tex]. Lets plug in the values:
[tex]x=2(24+30)[/tex]
[tex]x=108[/tex]
Now that we know that the larger rectangle has a perimeter of 108 and its shorter side is 24 inches, we can cross multiply to find our answer.
[tex]\frac{24}{108} =\frac{x}{27}[/tex]
Next we cross multiply. We multiply 108 and x, and we multiply 24 and 27.
[tex]108(x)=108x[/tex]
[tex]24(27)=648[/tex]
Now, lets put the values above back into the equation:
[tex]108x=648[/tex]
Our last step is to divide 648 by 108.
[tex]x=\frac{648}{108}[/tex]
[tex]x=6[/tex]
The length of the shorter side of the smaller rectangle is 6 inches.
