Q. 75.0( 4 Votes )

Two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 25. find the ratio of their corresponding heights.

Answer :


Let ABC and DEF are two isosceles triangles with AB =AC and DE = DF and A = D


Now, let AM and DN are their respective altitudes or heights.


Let ABC and DEF



A = D [given]


ABC ~DEF [by SAS similarity]


We know that, in similar triangles, corresponding angles are in the same ratio.


⇒∠B = E and C = F ……(i)


In ABM and DEN


B = E [from (i)]


and M = N [each 90°]


ABC ~ DEF [by AA similarity]


So, ……(ii)


We know that, the ratio of two similar triangles is equal to the square of the ratio of their corresponding sides.



[from (ii)]




Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Basic Proportionality TheoremBasic Proportionality TheoremBasic Proportionality Theorem42 mins
A Peep into Pythagoras TheoremA Peep into Pythagoras TheoremA Peep into Pythagoras Theorem43 mins
R.D Sharma | Solve Exercise -4.2 and 4.3R.D Sharma | Solve Exercise -4.2 and 4.3R.D Sharma | Solve Exercise -4.2 and 4.3FREE Class
NCERT | Strong Your Basics of TrianglesNCERT | Strong Your Basics of TrianglesNCERT | Strong Your Basics of Triangles39 mins
RD Sharma | Imp. Qs  From TrianglesRD Sharma | Imp. Qs  From TrianglesRD Sharma | Imp. Qs From Triangles41 mins
Quiz | Criterion of Similarity of TriangleQuiz | Criterion of Similarity of TriangleQuiz | Criterion of Similarity of Triangle45 mins
How to Ace Maths in NTSE 2020?How to Ace Maths in NTSE 2020?How to Ace Maths in NTSE 2020?36 mins
Know About Important Proofs in TrianglesKnow About Important Proofs in TrianglesKnow About Important Proofs in Triangles33 mins
Master BPT or Thales TheoremMaster BPT or Thales TheoremMaster BPT or Thales Theorem39 mins
Champ Quiz | Thales TheoremChamp Quiz | Thales TheoremChamp Quiz | Thales Theorem49 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses