How to work out a length on a similar triangle
with a question like this, you could get either:
- a large triangle with a smaller triangle inside it
- the tip of a smaller triangle balancing on the tip of the the larger one (or vice versa)
with the first option, you need to split these triangles into two separate trianlges and label the side lengths that you know of.
then you need to work out the ratio: find a side from each triangle that is the same side (but will obviously have different lengths) and divide the larger one by the smaller one to give you your ratio.
to find a length on the smaller triangle, you will need to divide the larger length from the same place by the ratio, eg., if your ratio is 1:2.5, divide the larger length by 2.5.
or if you need to find a longer length then you need to multiply your smaller length by the ratio.
we know the triangles from the last page are similar because they all have the same angles therefore we can work our their lengths.
ratio = 3:5 because that's the length of the smaller triange against the length of the larger triangle
or ratio = 1:1.6666...
therefore to find 'x' we need to 4/1.6666... = 2.4
these are a little easier because you just need to work out the ratio and then do you division or multiplication to get the other lengths.