[tex]\begin{gathered} x\text{ = 22 or -24} \\ \sin ce\text{ x cannot be negative, x = 22 is the correct answer} \end{gathered}[/tex]
Here, we want to find the value of x
Mathematically, when we have two similar shapes, the ratio of their corresponding sides are equal
Thus, we have it that;
[tex]\begin{gathered} \frac{24}{x+6}\text{ = }\frac{2x-8}{42} \\ \\ 24(42)\text{ = (x+6)(2x-8)} \\ 1008=2x^2-8x+12x-48 \\ 2x^2+4x-48-1008\text{ = 0} \\ 2x^2+4x-1056\text{ = 0} \\ \text{divide through by 2} \\ x^2\text{ + 2x-528 = 0} \\ x^2+24x-22x-528\text{ = 0} \\ x(x+24)-22(x+24)\text{ = 0} \\ (x-22)(x+24)\text{ = 0} \\ x-22\text{ = 0 or x +24 = 0} \\ x\text{ = 22 or x = -24} \end{gathered}[/tex]
x cannot be negative because if it is, x+6 and 2x-8 will be negative and it is not possible for the
