Understanding Similar Triangles in Geometry: A Grade 8 Math Concept

When dealing with similar triangles, we often find that their corresponding sides are in proportion. In this case, if one triangle has sides of length 3, 4, and 5, and is similar to another triangle with a longest side of 10, we can use the concept of proportionality to find the corresponding sides of the second triangle.

Using the concept of similarity, we can set up the following proportion:

$\frac{3}{x} = \frac{4}{y} = \frac{5}{10}$

Solving for x and y, we find that the sides of the second triangle are 6 and 8. Hence, the second triangle has sides of 6, 8, and 10.

Understanding the concept of similarity and applying proportionality allows us to solve such problems with ease.