Question

3. triangle ABC is Approximately equal to triangle JKL and AB= 2x+12. JK= 4x-50. find x and AB

Answer 1

In the following image we have a representation of the two triangles ABC and JKL:

The problem indicates that:

`AB=2x+12`

And:

`JK=4x-50`

Let's write that on our diagram for representation:

Since the two triangles approximately are equal, AB and JK are also approximately equal:

`AB\cong JK`

And thus:

`2x+12\cong4x-50`

Now we have to solve this equation for x.

Subtracting 2x to both sides:

`12\cong4x-2x-50`

Combine the like terms on the right side:

`12\cong2x-50`

Adding 50 to both sides:

`12+50\cong2x`

Adding the like terms on the left side:

`62\cong2x`

Dividing both sides by 2:

`\begin{gathered} (62)/(2)\cong x \\ 31\cong x \end{gathered}`

The value of x is 31.

The value of AB is:

`\begin{gathered} 2x+12 \\ \text{substituting x=31} \\ 2(31)+12 \\ 62+12 \\ 74 \end{gathered}`

AB is equal to 74.

Answer:

x=31

AB=74