Hello, Deb!

I *think* I've interpreted the problem correctly . . .

There is a right-angled triangle, base is 10cm plus 6cm, side is 12 cm, hypotenuese is unknown.

There is a line about two-thirds (at the 10 and 6) of the way from top to bottom which is x.

She needs to work out x.

The answer is 7.5cm but we don't know how to get that answer.

Not sure what you mean by "*about* two-thirds of the way from top to bottom".

But here's my diagram. Code:

*
| *
| *
| *
12 | | * x
| | *
| | *
* - - - - - * - - - - - - - *
10 6

Using Pythagorus: .$\displaystyle hyp^2 = 12^2 + 16^2 = 400\quad\Rightarrow\quad hyp = 20$

From the similar right triangles: .$\displaystyle \frac{x}{6} = \frac{20}{16}\quad\Rightarrow\quad x = 7.5$