216m²
Given that the sides of a triangle are in the ratio of 6:8:10 and their perimeter is equal to 720cm.
To find the area, we would use heron's formula which says area = √[s(s-a)(s-b)(s-c)] ,where a,b,c are the respective sides of the triangle and s = perimeter/2 but before that,we would need to find out the sides , for that , let's say the sides are equal to 6x ,8x & 10 x.
Then,
ATQ,
6x + 8x +10x = 720cm
24x = 720cm
x = 720cm/24
x = 30cm
therefore,
6x = 6*30cm = 180cm
8x = 8*30cm = 240cm
10x = 10*30cm = 300cm
and
s = 720cm/2 = 360cm
Now,
using heron's formula,
area = √[s(s-a)(s-b)(s-c)]
area = √[360cm(360cm-180cm)(360cm-240cm)(360cm-300cm)
area = √[360cm*180cm*120cm*60cm]
area = √(466,560,000cm⁴)
area = 21,600cm² or 216m²