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The sides of a triangle are in the ratio of 6:8:10 and its perimeter is 720 cm. Find its area.​

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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

User Mr Heelis
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