Triangles are defined as similar if all their corresponding angles are equal or if the lengths of their corresponding sides have the same ratios.
First, recall that in a right triangle, the two shorter sides intersect at the right angle.
if two similar figures have lengths in a given ratio (say A:B), then their areas will have a ratio that is the square of this length ratio (i.e.,A2:B2). Conversely, if the areas are in a given ratio, then the lengths will be in the square root of that ratio. ( Look at MGMAT CAT 4. q 19) Excellent example.