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

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

Answer 2

Option a.

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.

`(x)/(y) =(3)/(9)`

`(x)/(y) =(1)/(3)` ⇒ x =
`(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 =
`(2x+6)/(18+2y)`

=
`(2((y)/(3))+6)/(18+2y)` [as
`x=(y)/(3)`]

=
`(((2y+18))/(3) )/((18+2y))`

=
`(2y+18)/(3(18+2y))`

Ratio of P₁ and P₂ = (
`(1)/(3)`) ⇒ P₂ = 3P₁

Therefore, Option a is the answer.