The area of triangle is 216 cm2 and their sides are in the ratio 3 : 4 : 5. What is the perimeter of the triangle?

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Maha TAIT Official Paper (Held On 12 Dec 2017 Shift 2)
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  1. 6 cm
  2. 12 cm
  3. 36 cm
  4. 72 cm

Answer (Detailed Solution Below)

Option 4 : 72 cm
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Detailed Solution

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Concept:

Heron's formula for the area of a triangle.

\( Area=\sqrt{s(s-a)(s-b)(s-c)}\)

Here s is the semi-perimeter.

Solution:

Let the sides of the triangle be 3x, 4x, and 5x in cm.

Semi-perimeter = \(\frac{3x+4x+5x}{2}=6x\)

\( Area=\sqrt{6x(6x-3x)(6x-4x)(6x-5x)}\)

\(Area=6x^2\)

Also,

\(Area=6x^2=216\)

x = 6

Semi-perimeter = 6x = 36 cm

Perimeter = 72 cm.

Hence, option 4 is correct.

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