Similar Triangles and Side Lengths

CMAT 2026 · Quantitative Techniques & Data Interpretation · Medium · Geometry

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In triangles $ABC$ and $ADC$ , $\angle BAC = \angle ADC = 90^\circ$ . Also, $DC$ is 2 units long and $AC$ is 4 units long. What is the length of $BC$ ?

Geometric diagram showing right-angled triangles ABC and ADC with side lengths marked.

A.
8 units
B.
10 units
C.
$6\sqrt{3}$ units
D.
$12\sqrt{3}$ units

Answer

Explanation

Triangle $ADC$ is similar to Triangle $CAB$ by AAA similarity. $\frac{CD}{CA} = \frac{CA}{CB} \implies \frac{2}{4} = \frac{4}{BC} \implies BC = 8$ units.

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Similar Triangles and Side Lengths

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