In triangle BDC, a segment LM is drawn parallel to side BC. Find the length of the segment LN

univerkov | August 3, 2021 | education

In triangle BDC, a segment LM is drawn parallel to side BC. Find the length of the segment LN if it is known that BL = 15, LD = 10, BC = 34

Consider triangles DBC and LDM, in which, by condition, the bases of BC and LM are parallel.

Then the angle AMK and ABC are equal as the corresponding angles at the intersection of parallel straight lines. The angle D is common for the triangles, then the triangles DBC and LDM are similar in two angles.

Let us determine the length of the side BD. ВD = BL + LD = 15 + 10 = 25 cm.

Then the aspect ratio in similar triangles is:

LM / ВС = LD / ВD.

LM = ВС * LD / ВD = 34 * 10/25 = 13.6 cm

Answer: The length of the LM segment is 13.6 cm.

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