The length of BC given that the triangles are similar is: 8.2 cm.
How to Find the Length of Similar Triangles?
Triangles that are similar have corresponding congruent angles and corresponding sides lengths that have the same ratio. This means their corresponding side lengths are proportional to each other.
To find the missing lengths of any side lengths of the similar triangles with given area, we would have:
Area of triangle A/Area of triangle B = (side length of triangle A)²/(side length of triangle B)².
Given the following:
∆ABC is similar to ∆DEF
Area of ∆ABC = 64 cm²
Area of ∆DEF = 121 cm²
EF = 15.4 cm
BC = ?
Area of ∆ABC/Area of ∆DEF = length of side EF/length of side BC
Therefore:
121/64 = 15.4/BC
Cross multiply
BC = (15.4 × 64)/121
BC ≈ 8.2 cm
The length of BC, to the nearest tenth, is approximately 8.2 cm.
Learn more about similar triangles on:
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