Q. 135.0( 1 Vote )

# ΔABC is an isosceles triangle with AB = AC = 13 cm. The length of altitude from A on BC is 5 cm. Find BC. Given: ABC is an isosceles triangle with AB = AC = 13 cm

Suppose the altitude from A on Bc meets BC at M.

M is the midpoint of BC. AM = 5 cm

In ∆AMB, using Pythagoras theorem, we have

(Perpendicular)2 + (Base)2 = (Hypotenuse)2

(AM)2 + (BM)2 = (AB)2

(5)2 + (BM)2 = (13)2

(BM)2 = (13)2 – (5)2

(BM)2 = (13 – 5)(13+5)

[ (a2 – b2) = (a + b)(a – b)]

(BM)2 = (8)(18)

(BM)2 = 144

BM = ±12

BM = 12 [taking positive square root]

BC = 2BM or 2MC = 2×12 = 24cm

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 Theorem42 mins  Champ Quiz | Thales Theorem49 mins  NCERT | Strong Your Basics of Triangles39 mins  RD Sharma | Imp. Qs From Triangles41 mins  Quiz | Criterion of Similarity of Triangle45 mins  How to Ace Maths in NTSE 2020?36 mins  R.D Sharma | Solve Exercise -4.2 and 4.3FREE Class  R.D Sharma | Solve Exercise-4.545 mins  NCERT | Basic Proportionality Theorem22 mins  RD Sharma | Imp Qs Discussion- Triangles43 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 view all courses 