Maths · Co-ordinate of the centroid, orthocentre and circumcentre of a triangle
The sides of a triangle are and units, where The triangle is
The sides of a triangle are \( 3 x+ \) \( 4 y, 4 x+3 y \) and \( 5 x+5 y \) units, where \( \boldsymbol{x}, \boldsymbol{y}>0 . \) The triangle is
- A. right angled
- B. equilateral
- C. obtuse angled
- D. none of these
Step-by-step solution
Let sides be a=3x+4y, b=4x+3y, c=5x+5y. Since x,y>0, c is the longest. Compute a^2+b^2 = (3x+4y)^2 + (4x+3y)^2 = 9x^2+24xy+16y^2 + 16x^2+24xy+9y^2 = 25x^2+48xy+25y^2. c^2 = (5x+5y)^2 = 25x^2+50xy+25y^2. So c^2 > a^2+b^2, indicating an obtuse angle opposite side c. Hence the triangle is obtuse angled.
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