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The perimeter of a triangle is 16cm. One of the sides is of length 6cm. If the area of the triangle is 12sq.cm, then the triangle is

  • a)
    Rightangled

  • b)
    Isosceles

  • c)
    Equilateral

  • d)
    Scalene

Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The perimeter of a triangle is 16cm. One of the sides is of length 6cm...
Explanation:

  • Let the sides of the triangle be a, b, and c.

  • Given, perimeter of the triangle = a + b + c = 16cm.

  • Also, given one of the sides = 6cm.

  • Therefore, the sum of the other two sides = a + c = 16 - 6 = 10cm.

  • Let us assume that the height of the triangle corresponding to the side of length 6cm is h.

  • Area of the triangle = (1/2) * 6 * h = 12 sq.cm.

  • Therefore, h = 4cm.

  • Now, we can use the Heron's formula to find the lengths of the other two sides.

  • Semi-perimeter of the triangle = (a + b + c)/2 = 8cm.

  • Area of the triangle = sqrt(s(s-a)(s-b)(s-c)) = 12 sq.cm.

  • Substituting the values, we get (8-a)(8-b)(8-c) = 36.

  • As one of the sides is 6cm, let's assume a = 6.

  • Substituting the values, we get (8-6)(8-b)(8-c) = 36.

  • Simplifying the equation, we get (8-b)(8-c) = 18.

  • Now, we need to find the type of triangle.

  • If the triangle is isosceles, then b = c.

  • Substituting b = c in (8-b)(8-c) = 18, we get (8-b)(8-b) = 18.

  • Simplifying the equation, we get b = c = 5cm.

  • Therefore, the triangle is isosceles.


Hence, the correct answer is option 'B'.
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