Perpendicular to the height BD of the triangle ABC, the conduction intersects the side AB and BC at the point
August 8, 2021 | education
| Perpendicular to the height BD of the triangle ABC, the conduction intersects the side AB and BC at the point M and P. Find AB and the ratio of the rows of triangles MRB and ABC if it is known that MB = 7 BP = 9 PC = 18
Triangles ABC and MBP are similar, since the angle A is equal to the angle M, and the angle C is equal to the angle P. So, you can write down the ratio of their sides:
AB / MB = BC / BP.
Find aircraft:
BC = BP + PC = 9 + 18 = 27.
Find AB:
AB / 7 = 27/9;
AB = 27 * 7/9 = 21.
Area ratio of triangles:
S (ABC) / S (MBP) = k², where k is the coefficient of similarity of triangles. Find k:
k = AB / MB = 21/7 = 3;
S (ABC) / S (MBP) = 3² = 9.
Answer: side AB is 21, the ratio of the areas of triangles (ABC to MBP) is 9.
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