Question

Two rectangles are similar. If the height of the first rectangle is 3 inches, and the height of the second rectangle is 9 inches, how much longer is the second rectangle's perimeter? 3 times as long 6 times as long 9 times as long 6 inches longer

Answer 1

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.

$\frac{x}{y} =\frac{3}{9}$

$\frac{x}{y} =\frac{1}{3}$ ⇒ x = $\frac{y}{3}$

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 = $\frac{2x+6}{18+2y}$

                             = $\frac{2(\frac{y}{3})+6}{18+2y}$   [as $x=\frac{y}{3}$]

                            = $\frac{\frac{(2y+18)}{3} }{(18+2y)}$

                            = $\frac{2y+18}{3(18+2y)}$

Ratio of P₁ and P₂ = ($\frac{1}{3}$) ⇒ P₂ = 3P₁

Therefore, Option a is the answer.

Answer 2

3 times as long .....hope this helps