Question

Two similar rectangles have a scale factor of 1:3. The larges rectangle has a perimeter of 90 centimeters. What is the perimeter of the smaller rectangle

Answer 1

30 centimeters.

Explanation:

The scale between the rectangles is 1 to 3, so the larger one is three times bigger than the smaller one, that is, all the sides of the rectangle are three times bigger.

So, We know that the formula to calculate the perimeter of a rectangle is:

P = 2L + 2W

Where P is the perimeter, L is the lenght and W is the width.

If the lenght and the width of the bigger rectangle are three times bigger, we have that its perimeter, related to the perimeter of the smaller rectangle, will be:

(bigger rectangle: P1, L1 and W1; smaller rectangle: P2, L2 and W2)

P1 = 2*L1 + 2*W1 = 2*3*L2 + 2*3*W2 = 3*(2*L2 + 2*W2) = 3*P2

If P1 = 90 centimeters, we have that:

90 = 3*P2 -> P2 = 30 centimeters.

The perimeter of the smaller rectangle is 30 centimeters.