What is the ratio of the area of triangle XBY to the area of the triangle ABC for the given measurements, if XY is similar to AC, and XY=2 and AC=3
To find the ratio of the areas of two similar triangles, we can use the property that the ratio of the areas is equal to the square of the ratio of corresponding sides.
In this case, we are given that triangle XYB is similar to triangle ACB, with XY = 2 and AC = 3. We need to find the ratio of the area of triangle XBY to the area of triangle ABC.
The corresponding sides we are interested in are XY and AC. The ratio of XY to AC is 2/3.
Now, considering the areas, the ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides. Therefore, the ratio of the areas of triangle XBY to triangle ABC is (2/3)^2 = 4/9.
So, the ratio of the area of triangle XBY to the area of triangle ABC is 4/9, assuming that XY is similar to AC and XY = 2 and AC = 3.