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
1.3k views
in Triangles by (24.0k points)
closed by

A point within an equilateral triangle whose perimeter is 30 m is 2 m from one side and 3 m from another side. Find its distance from third side.

(a) √5 − 3 

(b) 5√3 − 3

(c) 5√5 − 3

(d) 5√3 - 3

1 Answer

+1 vote
by (23.5k points)
selected by
 
Best answer

(b) 5√3 – 5.

Given, ABC is an equilateral triangle such that AB = BC = CA = 10 m 

If O is any point in the ΔABC, then 

Area of ΔABC 

= Area (ΔOAB) + Area (ΔOAC) + Area (ΔOBC)

\(\frac{1}{2}\)x AB x OR + \(\frac{1}{2}\) x AC x OP + \(\frac{1}{2}\) x AC x OQ

\(\frac{1}{2}\) X AB x (OR + OP + OQ)        ( AB = BC = CA)

\(\frac{1}{2}\) x 10 x 2 (2 + 3 + OQ)

∵  Area of an equilateral Δ = \(\frac{\sqrt3}{4}\) (side)2

∴ \(\frac{\sqrt3}{4}\) x (10)2\(\frac{1}{2}\) x 10 x (5 + OQ)

⇒ 5√3 = 5 + OQ ⇒ OQ = 5√3 – 5.

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

...