Question

In the opposite figure the unit of length is the centimeter

(the points O K and P are collinear )
(the points O B and A are collinear)
(KB) and (PA) are parallel

OK=X,OP=Y
KB=5
KP=6
and PA=8
CALCULATE THE LENGTH OP​

Answer 1

see in the picture, we have: y = 6 + x

=> x = y - 6

because KB//PA, using Thales Theorem, we have:

`(ok)/(op) = (kb)/(pa) \\ \\ = > (x)/(y) = (5)/(8) \\ \\ < = > (y - 6)/(y) = (5)/(8) \\ \\ < = > 5y = 8(y - 6) \\ \\ < = > 5y = 8y - 48\\ \\ < = > 3y = 48 \\ \\ = > y = 16`

because OP = y => OP = 16