ABC is an isosceles triangle right-angled at B. Similar triangles ACD and ABE are constructed on side AC and AB. Find the ratio between the areas of triangle ABE and triangle ACD.

Explanation

`(ar (Delta ABC))/(ar (Delta ACD))=(AB^(2))/(AC^(2))=(AB^(2))/(2AB^(2))=(1)/(2) [ :. AC^(2)=AB^(2)+BC^(2)=2AB^(2)]`