Question

Find the length of ST

Answer 1

Answer:

$ST = 12$

Step-by-step 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.

$\dfrac{SR}{ST} = \dfrac{3}{4}$

Also,

$SR + ST = 21$

By a rule of proportions, you get

$\dfrac{SR + ST}{ST} = \dfrac{3 + 4}{4}$

$\dfrac{21}{ST} = \dfrac{7}{4}$

$7ST = 4 \times 21$

$7ST = 84$

$ST = 12$