MediumMathematicsHigh School (9–10)GeneralGeometry › TrianglesNumericalSAT

In triangle ABC, DE is parallel to BC. AD = x cm, DB = (x - 2) cm, AE = (x + 2) cm and EC = (x - 1)…

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In triangle $ABC$ , $DE$ is parallel to $BC$ . $AD = x$ cm, $DB = (x - 2)$ cm, $AE = (x + 2)$ cm and $EC = (x - 1)$ cm. Find $x$ , then $AB$ and $AC$ .

Need a reminder? The key ideaShow

The basic proportionality theorem. If $DE \parallel BC$ in triangle $ABC$ , with $D$ on $AB$ and $E$ on $AC$ , then $\dfrac{AD}{DB} = \dfrac{AE}{EC}$ . The same fact can be written $\dfrac{AD}{AB} = \dfrac{AE}{AC}$ . Triangles with the same height have areas in the ratio of their bases.

The worked solution

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