The value of length EC is 8
Similar triangles are triangles with equal corresponding angles and equal side ratio. What this means is that the ratio of the corresponding sides are equal.
Since DE is parallel to BC, the triangles ABC and ADE are similar.
let EC be x
15/27 = 10/10+x
15(10+x ) = 27 × 10
150 + 15x = 270
15x = 270 - 150
15x = 120
divide both sides by 15
x = 120/15
x = 8
Therefore the value of EC is 8