Question

Two squares are similar. The

scale factor from the first

square to the second square

is 1:3. If the perimeter of the

first square is 12 inches,

what is the perimeter of the

second square?

inches Fill in the

blank.

Answer 1

The perimeter of the second square is 36 inches

Explanation:

Given

Represent the sides of the squares with S1 and S2.

So:

`S_1:S_2 = 1 : 3` --- Scale factor

`P_1 =12` --- perimeter of the first

Required

Calculate P2, the perimeter of the second

Represent the ratios of the perimeter:

`Scale = P_1 : P_2`

Substitute 12 for P1

`Scale = 12 : P_2`

Equate both scale factors

`12 : P_2 = 1:3`

Convert to fraction

`(12)/(P_2) = (1)/(3)`

Cross multiply

`P_2 = 12 * 3`

`P_2 = 36`