Question

If the sides of a triangle are in the ratio 5 is to 4 is to 3 and its area is 54 CM square find perimeter ​

Answer 1

Perimeter = 36 cm

Explanation:

Ratio of sides = 5:4:3

Sides are:

a = 5x ; b= 4x ; c = 3x

Semi perimeter S = (a + b+ c )/2 = (5x + 4x +3x)/2 = 12x /2 = 6x

S - a = 6x - 5x = x

S - b = 6x - 4x = 2x

S - c = 6x - 3x = 3x

`Area=√(S*(S-a)*(S-b)*(S-c))\\\\√(6x*x*2x*3x)=54\\\\\sqrt{36x^(4)}=54\\\\6x^(2)=54\\\\x^(2)=(54)/(6)\\\\x^(2)=9\\\\x=√(9)\\\\ x=3\\`

sides of triangle:

a = 5x = 5*3 = 15 cm

b = 4x = 4*3 = 12 cm

c = 3x = 3*3 = 9 cm

Perimeter = 15 + 12 + 9 = 36 cm