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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.

Respuesta :

MrRoyal

Answer:

The perimeter of the second square is 36 inches

Step-by-step explanation:

Given

Represent the sides of the squares with S1 and S2.

So:

[tex]S_1:S_2 = 1 : 3[/tex] --- Scale factor

[tex]P_1 =12[/tex] --- perimeter of the first

Required

Calculate P2, the perimeter of the second

Represent the ratios of the perimeter:

[tex]Scale = P_1 : P_2[/tex]

Substitute 12 for P1

[tex]Scale = 12 : P_2[/tex]

Equate both scale factors

[tex]12 : P_2 = 1:3[/tex]

Convert to fraction

[tex]\frac{12}{P_2} = \frac{1}{3}[/tex]

Cross multiply

[tex]P_2 = 12 * 3[/tex]

[tex]P_2 = 36[/tex]

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