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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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
correct answer will be marked as brainlest
fast pls
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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.