Krishna
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Step 1:  Assume common ratio is x

NOTE: We know that there is a common ratio for all sides of the triangle.

That means that if that common ratio is denoted as x

Step 2: Write the lengths of the triangle using the variable(x).

EXAMPLE: Assume a = 3x, 4x, and 5x.

Step 3: Find the Area of the triangle

Step 1: Calculate the semi perimeter of the triangle.

NOTE: First calculate the perimeter of a triangle by adding up the length of

its three sides. Then, multiply by \frac {1}{2}

EXAMPLE: \frac{1}{2} (a+b+c)

\frac{1}{2}(3x+4x+5x)

s=\frac{1}{2}(12x)=6x

Step 2: Substitute the values of semi perimeter and lengths of the triangle in

the area formula

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

EXAMPLE:

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

Step 3: Calculate the values in parentheses.

EXAMPLE: [/math] \sqrt{6x(3x)(2x)(x)} [/math]

Step 4: Multiply the two values under the radical sign.Then, find their square

root.

EXAMPLE; = \sqrt{36 x^4}

=   6x^2

Step 4: Equate the calculated area and the given area measurement

6x^2 = 216 cm^2

x^2 = \frac{216}{6} = 36

x = 6

Step 5: Find the real lengths of the triangle by substitute the x value in the assumed lengths.

EXAMPLE:  3x = 3(6) = 18

4x = 4 (6) = 24

5x = 5 (6) = 30

Step 6:  Add all the lengths to know the perimeter of the circle

Perimeter = 18 + 24 + 30 = 72 cm

Therefore the pereimeter of the triangle = 72 cm