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
+1 vote
9.9k views
in Mathematics by (130k points)
edited by
ABC is an equilateral triangle of side 2a. Find each of its altitudes.

1 Answer

+1 vote
by (9.4k points)
selected by
 
Best answer

ABC is an equilateral triangle of side 2a. 

Draw, AD ⊥ BC

In ΔADB and ΔADC, we have

AB = AC [Given]

AD = AD [Given]

∠ADB = ∠ADC [equal to 90°]

Therefore, ΔADB ≅ ΔADC by RHS congruence.

Hence, BD = DC [by CPCT]

In right angled ΔADB, 

AB2 = AD2 + BD2

(2a)2 = AD2 + a

⇒ AD2  = 4a2 - a2

⇒ AD2  = 3a2 

⇒ AD  = √3a 

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

...