The areas of two similar triangles are 18 cm^2 and 8 cm^2. One of the sides of the first triangle is 4.5 cm. What is the length of the corresponding side of the other triangle?

3 cm

Step-by-step explanation:

The ratio of areas of similar figures is the square of the ratio of linear dimensions. That means the ratio of linear dimensions is the square root of the area ratio. The ratio of the smaller triangle dimensions to the larger is then ...

k = √ ((8 cm^2) / (18 cm^2)) = √ (4/9) = 2/3

Then the corresponding side of the smaller triangle is ...

... k · (4.5 cm) = (2/3) · (4.5 cm) = 3 cm