In similar triangles ABC and DEF, if side AB measures 6 cm and side DE measures 3 cm, how long is side BC if side EF measures 7 cm?

To find the length of side BC given the lengths of sides AB and DE along with side EF, we can utilize the property of similar triangles which states that the ratios of corresponding sides are equal.

First, establish the ratio of the sides given. Since triangles ABC and DEF are similar, we can write the ratio of the sides like this:

[

\frac{AB}{DE} = \frac{BC}{EF}

]

Substituting the known values:

[

\frac{6 \text{ cm}}{3 \text{ cm}} = \frac{BC}{7 \text{ cm}}

]

From the left side, we simplify the ratio:

[

\frac{6}{3} = 2

]

This tells us that for every 2 cm in triangle ABC, there is 1 cm in triangle DEF. Therefore, we have:

[

2 = \frac{BC}{7}

]

To find BC, we can cross-multiply:

[

BC = 2 \cdot 7

]

Calculating that gives:

[

BC = 14 \text{ cm}

]

Thus, the length of side BC is 14 centimeters. Understanding the properties of similar