# In a right-angled triangle ABC (angle C = 90 degrees) CD is perpendicular to AB; the ratio AC CB

August 31, 2021 | education

| **In a right-angled triangle ABC (angle C = 90 degrees) CD is perpendicular to AB; the ratio AC CB is equal to the ratio of 1 to 2. Find the ratio of the areas of the triangles ACD and CDB.**

Let the angle ABC = X0.

The sum of the acute angles of a right-angled triangle is 90, then the angle CAD = (90 – X) 0.

In a right-angled triangle BCD, the angle BCD = (90 – X) 0.

Then the right-angled triangles ACD and BCD are similar in acute angle.

By condition, BC / AC = 1/2, then the coefficient of similarity of triangles is K = 1/2.

The ratio of the areas of similar triangles is equal to the squared coefficient of their similarity.

Ssdv / Sasd = K2 = 1/4.

Answer: The area ratio is 1/4.

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