They are in ratio 4:3 so even the sides are in ratio.
Solve this with a proportion:
90:(10x-20) = 3:4
Multiply the means and extremes
3*(10x-20) and 4*90
30x-60 = 360
30x = 360+60
30x = 420
30x/30 = 420/30
x = 14
You can also solve it as an equation
since we said ab/bc = 3/4
[tex] \frac{90}{10x-20} = \frac{3}{4} [/tex]
Factorize 10x-20 as 10(x-2) and do LCM between denominators -> 20(x-2)
[tex] \frac{90}{10(x-2)} = \frac{3}{4} [/tex]
[tex] \frac{180}{20(x-2)} = \frac{15(x-2)}{20(x-2)} [/tex]
Multipli both fractions for 20(x-2) to delete denominator
Determine the range x-2 ≠ 0
x ≠ 2
180 = 15(x-2)
180 = 15x - 30
-15x = -30-180
-15x = -210
15x = 210
[tex] \frac{15}{15}x = \frac{210}{15} [/tex]
x = 14
