Question

angle M =angle N=46°.Express x in terms of a,b,c where a,b,c are length of LM,MN,NK respectively?

Answer 1

GIVEN:
∠KNP =∠ KML = 46°
LM = a , MN = b , NK = c

In  ∆KPN  and ∆KLM,
∠ KNP = ∠KML = 46°    [ given]
∠ K =  ∠ K      [Common]

∆KPN  ~ ∆KLM   [by AA similarity criterion  of triangles]

KN/ KM = NP/ML  [corresponding sides of similar triangles are proportional]

c /(b+c) = x/a      [KM = MN + NK]
x(b+c) = c×a     
x = ac/ (b+c)

Hence, the value of x = ac/(b+c)

Answer 2

Explanation:

GIVEN:

∠KNP =∠ KML = 46°

LM = a , MN = b , NK = c

In  ∆KPN  and ∆KLM,

∠ KNP = ∠KML = 46°    [ given]

∠ K =  ∠ K      [Common]

∆KPN  ~ ∆KLM   [by AA similarity criterion  of triangles]

KN/ KM = NP/ML  [corresponding sides of similar triangles are proportional]

c /(b+c) = x/a      [KM = MN + NK]

x(b+c) = c×a     

x = ac/ (b+c)

Hence, the value of x = ac/(b+c)

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