Answer:
235.15 sq.cm
Step-by-step explanation:
Perimeter:
Perimeter of a triangle is sum of all three sides.
Ratio of sides = 5 : 6 : 7
Sides are 5x , 6x , 7x
Perimeter = 72 cm
5x + 6x + 7x = 72
Combine like terms.
18x = 72
Divide both sides by 18,
x = 72÷ 18
x = 4
5x = 5*4 = 20 cm
6x = 6*4 = 24 cm
7x = 7*4 = 28 cm
Sides: 20cm , 24 cm , 28 cm
So, it is a scalene triangle.
To find the area of scalene triangle use Heron's formula.
a = 20 cm ; b = 24 cm and c = 28 cm
[tex]\sf s = \dfrac{a + b+ c}{2} \ where \ s \ is \ the \ semi \ perimeter.[/tex]
[tex]\sf =\dfrac{72}{2}\\\\\\ = 36 \ cm[/tex]
s - a = 36 - 20 = 16 cm
s -b = 36 - 24 = 12 cm
s - c = 36 - 28 = 8 cm
[tex]\sf \boxed{Area = \sqrt{s(s-a)(s-b)(s-c)}}[/tex]
[tex]\sf =\sqrt{36*16*12*8}\\\\ = 6*4*4\sqrt{6}\\\\= 96 *2.45\\\\=235.15 \ cm^2[/tex]
