The area of the triangle is 9000 square centimeters
How to determine the area?
Let the sides in order of length be represented as:
x, y and z.
So, we have:
z = 80 + y
z = 130 + x
P = 540
The perimeter is calculated as:
P = x + y + z
So, we have:
x + y + z =540
Substitute z = 130 + x
x + y + 130 + x =540
Evaluate the like terms
2x + y = 410
Substitute z = 130 + x in z = 80 + y
130 + x = 80 + y
Evaluate the like terms
x - y = -50
So, we have:
2x + y = 410
x - y = -50
Add both equations
3x = 360
Divide by 3
x = 120
Substitute x = 120 in z = 130 + x
z = 130 + 120
z = 250
Substitute z = 250 in z = 80 + y
250 = 80 + y
y = 170
So, we have:
x = 120
y = 170
z = 250
The area is then calculated as:
[tex]Area = \sqrt{s * (s -x) *(s - y) * (s -z)[/tex]
Where
s = P/2 = 540/2
s = 270
So, we have:
[tex]Area = \sqrt{270 * (270 -120) *(270 - 170) * (270 -250)[/tex]
Evaluate
Area = 9000
Hence, the area of the triangle is 9000 square centimeters
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