# The vertices of a triangle are the points with coordinates (3, 5), (9, 13), (10, 6). Prove that the triangle is isosceles. Calculate is area.

The three vertices are (3, 5), (9, 13), (10, 6)

Length of first side = √((9 - 3)2 + (13 - 5)2)

Length of first side = √(62 + 82)

Length of first side = 10 units

Length of second side = √((10 - 9)2 + (6 - 13)2)

Length of second side = √(12 + 72)

Length of second side = √50 units

Length of third side = √((10 - 3)2 + (6 - 5)2)

Length of third side = √(72 + 12)

Length of third side = √50 units

Since the length of second and third sides are equal so the triangle is isosceles

Length of height Length of height = √75 units

Area = 0.5 × base × height

Area = 12.5 × 1.732

Area = 12.5 × 1.732 = 10.768 sq. units

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Relationship Between Coefficients and Zeros44 mins  Quiz on Important Algebra Questions26 mins  Section Formula30 mins  Quiz on Number of Solutions of an Equation24 mins  Important Algebra Questions46 mins  Interactive Quiz: Algebra Important Questions38 mins  Genius Quiz | NTSE Questions Algebra27 mins  Previous Year RMO Questions43 mins  NCERT | Most Important Proofs for Boards28 mins  Interactive Quiz: Nature of Roots51 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 