A straight line parallel to side AC of triangle ABC intersects sides AB and BC at points M
| April 12, 2021 | education
A straight line parallel to side AC of triangle ABC intersects sides AB and BC at points M and H, respectively, MB = 2 cm, AM = 14 cm, MH = 4 cm What is the length of side AC?
This is almost a typical task like triangles. Since the straight line МН is parallel to the side АС, then by definition МН cuts off a similar triangle МН from the triangle ABC. And in such triangles, the sides opposite to equal angles are proportional. Or, switching to the language of formulas, we get:
AB: MB = AC: MH, whence AC = AB * MN: MB.
In this proportion for finding the AC, the value of AB is unknown, which is not difficult to find by its components AM and MB.
AB = AM + MB = 14 cm + 2 cm = 16 cm.
AC = 16 cm * 4 cm: 2 cm = 32 cm.
Answer: AC = 32 cm.
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