Respuesta :
The ratio between the lengths of 2 rectangles is the same between their perimeters
[tex]l_1\colon l_2=P_1\colon P_2[/tex]Since the ratio between the length of rectangle A and the length of rectangle B is 7: 3, then
The ratio between the perimeter of rectangle A to the perimeter of rectangle B is 7: 3 too
[tex]\begin{gathered} l_A\colon l_B=7\colon3 \\ P_A\colon P_B=7\colon3 \end{gathered}[/tex]Since the perimeter of rectangle A is 540, then
[tex]540\colon P_B=7\colon3[/tex]We will write them as a fraction
[tex]\frac{540}{P_B}=\frac{7}{3}[/tex]By using the cross multiplication
[tex]\begin{gathered} P_B\times7=540\times3 \\ 7P_B=1620 \end{gathered}[/tex]Divide both sides by 7
[tex]\begin{gathered} \frac{7P_B}{7}=\frac{1620}{7} \\ P_B=231.4285714 \end{gathered}[/tex]Round it to the nearest tenth
[tex]P_B=231.4\text{ inches}[/tex]The perimeter of the smaller rectangle B is 231.4 inches
