Question

the figures below are similar. the labeled sides are corresponding.
5 mm
6 mm
what is the ratio of the area of the smaller square to the area of the larger square?
write your answer as the ratio of two whole numbers separated by a colon (for exampl
2:3).

Explanation:

Step1: Calculate the area of the smaller square

The side length of the smaller square is \(s_1 = 5\) mm. The area of a square is \(A = s^2\), so \(A_1=5^2 = 25\) \(mm^2\).

Step2: Calculate the area of the larger square

The side length of the larger square is \(s_2 = 6\) mm. Using the area formula \(A = s^2\), we get \(A_2 = 6^2=36\) \(mm^2\).

Step3: Find the ratio of the areas

The ratio of the area of the smaller square to the area of the larger square is \(\frac{A_1}{A_2}=\frac{25}{36}\), which in ratio form is \(25:36\).

Answer:

\(25:36\)