Q. 43.7( 3 Votes )

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.

Answer :

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


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