In the following image we have a representation of the two triangles ABC and JKL:
The problem indicates that:
[tex]AB=2x+12[/tex]
And:
[tex]JK=4x-50[/tex]
Let's write that on our diagram for representation:
Since the two triangles approximately are equal, AB and JK are also approximately equal:
[tex]AB\cong JK[/tex]
And thus:
[tex]2x+12\cong4x-50[/tex]
Now we have to solve this equation for x.
Subtracting 2x to both sides:
[tex]12\cong4x-2x-50[/tex]
Combine the like terms on the right side:
[tex]12\cong2x-50[/tex]
Adding 50 to both sides:
[tex]12+50\cong2x[/tex]
Adding the like terms on the left side:
[tex]62\cong2x[/tex]
Dividing both sides by 2:
[tex]\begin{gathered} \frac{62}{2}\cong x \\ 31\cong x \end{gathered}[/tex]
The value of x is 31.
The value of AB is:
[tex]\begin{gathered} 2x+12 \\ \text{substituting x=31} \\ 2(31)+12 \\ 62+12 \\ 74 \end{gathered}[/tex]
AB is equal to 74.
Answer:
x=31
AB=74
