ABC is an isosceles triangle, right-angled at B. Similar triangles ACD and ABE are constructed on sides AC and AB. Find the ratio between the areas of ΔABE and ΔACD.
ΔABC is right triangle.
Applying Pythagoras theorem we get,
AC2 = AB2 + BC2 {∵ AB = BC}
⇒ AC2 = 2AB2
Given that the two triangles ΔACD and ΔABE are similar.
We know that if two triangles are similar then the ratio of their areas is equal to the ratio of the squares of their corresponding altitudes.
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