In triangle ABC AB = 15m, AC = 20m, BC = 32m. On the side AB there is a segment AD = 9m, and on the side AC
| September 10, 2021 | education
In triangle ABC AB = 15m, AC = 20m, BC = 32m. On the side AB there is a segment AD = 9m, and on the side AC – a segment AE = 12m. Find DE and the ratio of the areas of triangles ABC and ADE.
Let us prove that triangles ABC and ADE are similar.
Determine the ratio of the sides of the triangles.
AD / AB = 9/15 = 3/5.
AE / AC = 12/20 = 3/5.
Angle A is common for triangles.
Then the triangles ABC and ADE are similar in two proportional sides and the angle between them.
DE / BC = 3/5.
DE = 3 * BC / 5 = 3 * 32/5 = 19.2 m.
The ratio of the areas of similar triangles is equal to the squared coefficient of their similarity.
Sade / Savs = 9/25.
Answer: The length of the DE is 19.2 cm, the area ratio is 9/25.
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