Question

Find the length of ST

Answer 1

`ST = 12`

Explanation:

By AA Similarity, triangles ASR and EST are similar.

The ratio of the lengths of the sides of triangle ASR to those of EST is 6/8 or 3/4.

`(SR)/(ST) = (3)/(4)`

Also,

`SR + ST = 21`

By a rule of proportions, you get

`(SR + ST)/(ST) = (3 + 4)/(4)`

`(21)/(ST) = (7)/(4)`

`7ST = 4 * 21`

`7ST = 84`

`ST = 12`