math problem. please help.?

Question

answer this for me pleasee! i want to see if im correct or not.

the second side of a triangle is four more than the first side, and the third side is five more than the second. if the product of the first and third sides is added to the product of the second and third sides, the result is 124 more than twice the square of the first side. find the perimeter of the triangle.

Answer 1

let the sides b a.b.c
b=a+4
c=b+5=a+9
ac+bc=124+a^2
a(a+9)+(a+4)(a+9)=124+2a^2
thus a=4,b=8,c=13
peremetr=25

Answer 2

let x , y and z be the length of the three sides

"the second side of a triangle is four more than the first side" tells you: y = x + 4

"third side is five more than the second" tells you:
z = y + 5

" the product of the first and third sides is added to the product of the second and third sides, the result is 124 more than twice the square of the first side" tells you

xz + yz = 2x^2 + 124

so you have 3 equations

y = x + 4
z = y + 5
xz + yz = 2x^2 + 124

z = x + 4 + 5
z = x + 9

x(x + 9) + (x + 4)(x + 9) = 2x^2 + 124
x^2 + 9x + x^2 + 13x + 36 = 2x^2 + 124
2x^2 + 22x + 36 = 2x^2 + 124
22x + 36 = 124
22x = 88
x = 4

y = x + 4
y = 4 + 4
y = 8

z = x + 9
z = 4 + 9
z = 13

so the three sides are 4, 8 and 13

the perimeter is 4 + 8 + 13 = 25

Answer 3

b = a + 4
c = b + 5
ac + bc = a^2 + 124
c(a + b) = a^2 + 124
(b + 5)(a + b) = 2a^2 + 124
(a + 4 + 5)(a + a + 4) = 2a^2 + 124
(a + 9)(2a + 4) = 2a^2 + 124
2a^2 + 22a + 36 = 2a^2 + 124
22a = 88
a = 4
b = 8
c = 13
P = 25

Answer 4

Perimeter is 25