Question

What is value of x?
Enter your answer in the box.

Answer 1

`x \ = \ 10`

Explanation:

Let point
`D` be the point where the straight line drawn from point
`A` meets the straight line
`BC`, it is evident that
`\triangle ABD` and
`\triangle ACD` is similar given that both triangles share the same angle,
`\angle BAD \ = \ \angle DAC`. Hence, the ratio of the sides of each triangle is the same. Specifically,

`\displaystyle{(x+4)/(8) \ = \ (2x+1)/(12)}`.

Performing cross multiplication yields

`12\left(x+4\right) \ = \ 8\left(2x+1\right) \\ \\ \rule{0.15cm}{0cm}12x+48 \ = \ 16x+8 \\ \\ \rule{1.1cm}{0cm} 4x \ = \ 40 \\ \\ \rule{1.3cm}{0cm} x \ = \ 10`.