The right-angled triangle ABC is such that ∠B = 90°. Point D is picked on BC such that triangles ABC and DBA are similar. If AB : BC = m : n, what is △ABC : △ABD, where △ denotes the area of a triangle?

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Q: 58 (CAPF/2023)
The right-angled triangle ABC is such that ∠B = 90°. Point D is picked on BC such that triangles ABC and DBA are similar.
If AB : BC = m : n, what is △ABC : △ABD, where △ denotes the area of a triangle?

question_subject: 

Mathematics

question_exam: 

CAPF

The areas of similar triangles are proportional to the squares of corresponding sides. Hence, (m+n)² : n² correctly represents the area ratio.