Question

The side of a triangle are in the ratio 5 is to 12 is to 13 and its perimeter is 1550 m find the area of triangle

Answer 1

Answer :

Let the sides of the triangle in ratios be 5a , 12a and 13a

Perimeter = 5a + 12a + 13a = 1550m

30a =1550

a = 51.67

Sides are 258.35 m , 620.04 and 671.71

Area by Heron's Formula ,

s = Perimeter/2 = 1550/2 = 775

s-a = 775 - 258.35 = 516.65

s-b = 775 - 620.04 = 154.96

s-c = 775 - 671.71 = 103.29

Area of triangle = \sqrt{s*(s-a)*(s-b)*(s-c)}

$=\sqrt{775*516.65*154.96*103.29} = \sqrt{6408789709.179} = 80054.91m^{2}$