Answer:
Option a.
Step-by-step explanation:
Two rectangles are similar. Height of one rectangle is 3 inches and height of second rectangle is 9 inches.
Let width of rectangles are x inches and y inches.
Then width of the second rectangle will be in the same ratio as of their heights.
[tex]\frac{x}{y} =\frac{3}{9}[/tex]
[tex]\frac{x}{y} =\frac{1}{3}[/tex] ⇒ x = [tex]\frac{y}{3}[/tex]
Now perimeter of first rectangle P₁ = 3 + 3 + x + x = 2x + 6
Perimeter of second rectangle P₂ = 9 + 9 + y + y = 18 + 2y
Ratio of P₁ and P₂ = [tex]\frac{2x+6}{18+2y}[/tex]
= [tex]\frac{2(\frac{y}{3})+6}{18+2y}[/tex] [as [tex]x=\frac{y}{3}[/tex]]
= [tex]\frac{\frac{(2y+18)}{3} }{(18+2y)}[/tex]
= [tex]\frac{2y+18}{3(18+2y)}[/tex]
Ratio of P₁ and P₂ = ([tex]\frac{1}{3}[/tex]) ⇒ P₂ = 3P₁
Therefore, Option a is the answer.
