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In the adjoining figure, find AC. |
Answer» From the given figure ΔABC, DE || BC. Let EC = x cm. We know that basic proportionality theorem states that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio. Then \(\frac{AD}{DB}\) = \(\frac{AE}{EC}\) ⇒ \(\frac{6}9\) = \(\frac{8}x\) ⇒ x = \(\frac{8(9)}{6}\) ⇒ x = 12 cm = EC Here, AC = AE + EC ⇒ AC = 8 + 12 = 20 cm ∴ AC = 20 cm |
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