Question

if aq= 6, cq = 8, and bq = 4, then eq = ?

Answer 1

If EQ is parallel to AC, and the angle AQC is 90°, then, applying Pythagorean theorem, we can find the base AC:

$$AC=\sqrt{6^2+8^2}=10.$$

Then, since triangles ABC and BQE are similar, we understand that

$$\frac{AC}{QE}=\frac{AB}{BQ},\\\space\\ QE=AC\cdot\frac{BQ}{AB}=10\frac{4}{6+4}=4.$$