The areas of two right-angled triangles with respectively equal acute angles are 2/3. how the hypotenuses of these triangles relate.
| February 20, 2021 | education
Since, by condition, the acute angles of the triangles are equal, the angle BAC = B1A1C1, then the right-angled triangles ABC and A1B1C1 are similar in acute angle.
By condition, Sa1v1s1 / Saavs = 2/3.
The ratio of the areas of similar triangles is equal to the squared coefficient of their similarity.
Sa1b1s1 / Saabs = K ^ 2 = 2/3.
Then K = √ (2/3).
The ratio of the hypotenuses of similar triangles is equal to the coefficient of similarity.
A1C1 / AC = √ (2/3).
Answer: The hypotenuses of triangles are referred to as √ (2/3).
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