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The sides of a triangle are in the ratio 12:15:27 and it's perimeter is 540 cm . find its area

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Explanation

The sides of a triangle are in a ratio 12 : 15 : 27 and the perimeter of the triangle is 540 cm.

Let the sides of the triangle be x, y and z respectively.

x : y : z = 12 : 15 : 27

Meaning that if the common factor for the sides is a

x = 12a

y = 15a

z = 27a

The perimeter of a figure is the sum of all of its exterior dimensions.

So, the perimeter of the given triangle is

x + y + z = 540

If we replace x, y and z with 12a, 15a and 27a, we can get the common factor a and obtain the dimensions of the triangle.

x + y + z = 540

12a + 15a + 27a = 540

54a = 540

Divide both sides by 54

(54a/54) = (540/54)

a = 10 cm

x = 12a = 120 cm

y = 15a = 150 cm

z = 27a = 270 cm

Hence, we can now easily obtain the area of the triangle.

The area of a triangle given the three sides of the triangle is given through Heron's formula as

Area = √[p(p−x)(p−y)(p−z)]

where p = half of the perimeter of the triangle

p = (x + y + z)/2

x = 120, y = 150, z = 270

p = (120 + 150 + 270)/2 = 270 cm

Area = √[p(p−x)(p−y)(p−z)]

Area = √[270 × (270 − 120) × (270 − 150) × (270 − 270)]

Area = √[270 × 150 × 120 × 0]

= √(0)

= 0 cm²

Hope this Helps!!!

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