Given: △klm, km=48, ld=16
ld⊥km, nops - rectangle no: op=5: 9 find: no, op

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