Answer
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!!!