A plane parallel to side AB of triangle ABC intersects its sides AC and BC at points D and E, respectively.

| July 7, 2021 | education

A plane parallel to side AB of triangle ABC intersects its sides AC and BC at points D and E, respectively. Find the length of the side AB if DE = 6cm, AD = 4cm and CD = 12cm.

When the triangle ABC intersects with a parallel plane at points D and E, two triangles are formed – ABC and CDE. These triangles have equal angles: CAB = CDE and ABC = DEC. And also in the condition it is indicated that the sides AD = 4 cm, and CD = 12 cm. The side AC, therefore, is the sum of these segments, i.e. 16 cm.

Note that these triangles ABC and CDE are similar.

Similar triangles are triangles, the angles of which are respectively equal, and the sides of one triangle are proportional to the similar sides of the other triangle.

Accordingly, the aspect ratio of AC and AD will be the same as the aspect ratio of AB and DE. Let’s make the proportion:

12/16 = 6 / AB

AB = 16 * 6/12 = 8

Answer: AB = 8 cm



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