Question

the area of a triangle is 150 cm square and its sides are in the ratio 3 ratio 4 ratio 5 what is its perimeter​

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

Perimeter = 15+20+25 = 60 cm

Answer 2

The perimeter of a triangle is 60 cm

Step-by-step explanation:

let the sides be a= 3x,b=4x and c= 5x

using herons formula

perimeter = 3x+4x+5x

semi perimeter = $\frac{3x+4x+5x}{2}$ = $\frac{12x}{2}$ = 6x

then area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

150 = $\sqrt{6x(6x-3x)(6x-4x)(6x-5x)}$

150 = $\sqrt{6x\times 3x\times 2x \times x}$

150 = $\sqrt{2\times3\times3\times2\timesx\times x\times x\times x\times x}$

150 = 6x²

x² =$\frac{150}{6}$

x² =25

x =√25

x= 5 cm

putting the value of x in sides

a= 3x = 3× 5 = 15 cm

b= 4x = 4×5 = 20 cm

c = 5x = 5×5 = 25 cm

then perimeter = a+b+c = 15 +20+25 = 60 cm

hence ,

The perimeter of a triangle is 60 cm

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