Respuesta :
ANSWER:
G. 42 feet
STEP-BY-STEP EXPLANATION:
Given:
L1 = 4 ft
P1 = 14 ft
W2 = 9 ft
We know that the perimeter is the sum of all the sides. With this we can calculate the width of the first rectangle, like this:
[tex]\begin{gathered} P_1=L_1+L_1+W_1+W_1 \\ 2\cdot W_1=P_1-2L_1 \\ W_1=\frac{P_1-2L_1}{2} \\ \text{we replacing} \\ W_1=\frac{14-2\cdot4}{2}=\frac{14-8}{2}=\frac{6}{2} \\ W_1=3\text{ ft} \end{gathered}[/tex]Since they are similar, we can calculate the ratio between rectangles, calculating the ratio between widths like this:
[tex]r=\frac{W_2}{W_1_{}}=\frac{9}{3}=3[/tex]We can calculate the length of the second rectangle with the help of the ratio, just like this:
[tex]\begin{gathered} r=\frac{L_2}{L_1} \\ L_2=r\cdot L_1=3\cdot4 \\ L_2=12\text{ ft} \end{gathered}[/tex]Therefore, now if we can calculate the perimeter of the second rectangle:
[tex]\begin{gathered} P_2=L_2+L_2+W_2+W_2 \\ \text{ we replacing} \\ P_2=12+12+9+9 \\ P_2=42\text{ ft} \end{gathered}[/tex]Therefore the perimeter of the similar rectangle is 42 feet.
