Question

Area of triangle is 150 ratio is 3x,4x,5x

Answer 1

Let coefficient of ratios be X

a = 3x

b = 4x

c = 5x

Using Heron's Formula,

s = (3+4+5)x/2 = 12x/2 = 6x

\sqrt{s(s - a)(s - b)(s - c)} \\ \sqrt{6x(6x - 3x)(6x - 4x)(6x - 5x)} \\ \sqrt{6x \times 3x \times 2x \times x} \\ \sqrt{36 {x}^{4} } \\ 6 {x}^{2} \\ area \: given = 150 \: {cm}^{2} \\ so. \\ 6 {x}^{2} = 150 \\ {x}^{2} = \frac{150}{6} \\ {x}^{2} = 25 \\ x = \sqrt{25} = 5 \: cm

Now,

a = 5*3 = 15 cm

b = 5*4 = 20 cm

c = 5*5 = 25 cm