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AP EAMCET2002MathematicsProperties of Triangles

The perimeter of a triangle is 16 ~cm , one of the sides is of length 6 ~cm . If the area of the triangle is 12 sq cm . Then the triangle is

Options

  1. Aright angled
  2. Bisosceles
  3. Cequilateral
  4. Dscalene

Correct answer

B. isosceles

Step-by-step solution

Given that aligned & 2 s=16 s=8 ~cm & 2 s=a+b+c, a=6 ~cm , =12 & ^2=s(s-a)(s-b)(s-c) & 144=8(8-6)(8-b)(8-c) & [ array r a+b+c=16 b+c=10 b=10-c array ] & 18=2(8-b)(8-c) & 18=2(8-10+c)(8-c) & 9=(-2+c)(8-c) & 9=-16+10 c-c^2 c^2-10 c+25=0 & (c-5)^2=0 & c=5 & aligned Then, b=10-5=5 b=c Therefore, triangle is isosceles.

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