If ABC and DEF are two isosceles right triangles such that begin mathsize 12px style AB over DE equals 3 over 4 end style. Find the ratio of their areas.

Asked by Topperlearning User | 3rd Oct, 2017, 01:37: PM

Expert Answer:

 

Since, ABC and DEF are isosceles right triangles , they must be equiangular, as their angles must be begin mathsize 12px style 45 degree comma space 45 degree comma space 90 degree end style.

So we see that both the triangles are similar (AAA rule)

Hence the ratio of their areas is the same as the ratio of  the squares of their corresponding sides.

begin mathsize 12px style Hence comma space fraction numerator straight A left parenthesis increment ABC right parenthesis over denominator straight A left parenthesis increment DEF right parenthesis end fraction equals 9 over 16. end style


Answered by  | 3rd Oct, 2017, 03:37: PM