Verified answer

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The sides of a triangle are in the ratio 12: 17: 25 and its perimeter is 540 cm

The area is: (a) 1000 sq. cm (b) 2000 sq. cm (c)9000 sq. cm (d) 4000 sq. cm

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option (c) 9000 sq. cm.

Step-by-step explanation:

To find the area of the triangle, we can use Heron's formula. Heron's formula states that the area of a triangle with sides a, b, and c, and semi-perimeter s, is given by:

*Area = sqrt(s(s-a)(s-b)(s-c))*

where *s = (a + b + c) / 2* is the semi-perimeter of the triangle.

In this case, the sides of the triangle are in the ratio 12:17:25, and the perimeter is given as 540 cm. We can set up the following equation:

*12x + 17x + 25x = 540*

Simplifying the equation, we get:

*54x = 540*

Dividing both sides by 54, we find:

*x = 10*

Now, we can calculate the lengths of the sides of the triangle:

__Side 1 = 12x = 12 _ 10 = 120 cm_*

__Side 2 = 17x = 17 _ 10 = 170 cm_*

__Side 3 = 25x = 25 _ 10 = 250 cm_*

Next, we can calculate the semi-perimeter of the triangle:

*s = (120 + 170 + 250) / 2 = 540 / 2 = 270 cm*

Finally, we can calculate the area using Heron's formula:

__Area = sqrt(270(270-120)(270-170)(270-250)) = sqrt(270 _ 150 _ 100 _ 20) = sqrt(810000000) = 9000 cm^2_*

Therefore, the area of the triangle is *9000 sq. cm*. So, the correct answer is option (c) 9000 sq. cm.