A rhombus ADFE is inscribed in triangle ABC so that angle A at the bottom is common
January 25, 2021 | education
| A rhombus ADFE is inscribed in triangle ABC so that angle A at the bottom is common, and the opposite vertex F lies on the side of triangle BC. find the perimeter of the rhombus if AB = 3 cm, AC = 7 cm.
Since ADFE is a rhombus, DF is parallel to AE and AC.
Then triangles ABC and BDF are similar in two angles.
The angle B in triangles is common, the angle ВDF = BAC as the corresponding angles at the intersection of parallel straight lines АС and DF secant AB.
Let AD = DF = FE = AE = X cm.
Then BD = AB – AD = 3 – X cm.
From the similarity of triangles: AB / AC = BD / DF.
3/7 = (3 – X) / X.
21 – 7 * X = 3 * X.
10 * X = 21.
X = 2.1 cm.
Then Radfe = 4 * X = 4 * 2.1 = 8.4 cm.
Answer: The perimeter of the rhombus is 8.4 cm.
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