Question

if the area of a triangle is 150 and its sides are in ratio 3:4:5 then find the perimeter of triangle​

Answer 1

Answer:

60

Step-by-step explanation:

3x+4x+5x=perimeter

12x=p ----------1

150=root(s(s-3x)(s-4x)(s-5x))

22500=6x*3x*2x*x

22500=36x*x^4

625=x^4

x=5

by 1

p=60

Answer 2

$let \: the \: sides \: be \: 3x \: 4x \: and \: 5x \\ s = \frac{3x + 4x + 5x}{2} = 6x \\ \\ area \: \: \: \: \: \:= \sqrt{6x(6x - 3x)(6x - 4x)(6x - 5x)} \\ \\ = > 150 = \sqrt{6x \times 3x \times 2x \times x} \\ \\ = > 150 = \sqrt{36 {x}^{4} } \\ \\ = > 150 = 6 {x}^{2} \\ \\ = > x \: \: \: = \sqrt{25} \\ \\ = > x \: \: \: = 5 \\ \\ therefore \: the \: side \: are \: \\ 3x = 15 \\ 4x = 20 \\ 5x= 25 \\ perimeter \: = 15 + 20 + 25 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 60 \: units$