Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
4.2k views
in Triangles by (55.4k points)
closed by

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

1 Answer

+1 vote
by (50.2k points)
selected by
 
Best 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

AB/DE = AC/DF

∠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, AM/DN = AB/DE = BM/EN ……(ii)

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

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...