Answer:
NO = 10 and OP = 18
Step-by-step explanation:
Given: KM = 48 , LD = 16 , NO : OP = 5 : 9 and NOPS is rectangle.
To find: Value of NO and OP
Let the value of NO and OP = 5x and 9x
frst we prove ΔKLD is similar to ΔKON and ΔMLD is similar to ΔMPS
In ΔKLD and ΔKON
∠KDL = ∠KNO = 90° ( corresponding angles )
∠DKL = ∠NKO ( common Angle )
⇒ ΔKLD is similar to ΔKON by AA similarity rule.
⇒
subtract 1 from both sides
⇒
⇒
by substituting value from figure,
⇒
⇒ ..................... (1)
In ΔMLD and ΔMPS
∠MDL = ∠MSP = 90° ( corresponding angles )
∠DML = ∠SMP ( common Angle )
⇒ ΔMLD is similar to ΔMPS by AA similarity rule.
⇒
subtract 1 from both sides
⇒
⇒
by sustituting value from figure,
⇒
⇒ ..................... (2)
Add eqn. (1) & (2), we get
( from figure KN + SM = KM - NS)
substitute given values,
x = 2
⇒ NO = 5x = 5 × 2 = 10
⇒ OP = 9x = 9 × 2 = 18