Question

ABCD is trapezium in which AB//CD. line seg RN and LM ARE DRAWN PARALLEL TO AB SUCH THAT AJ=JK=KP. IF AB=0. 5M AND AP=BQ=1. 8M FIND LENGTH OF AC, BD,RN, LM?

Answer 1

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Answer 2

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AP = 1.8 m

JK = AJ =KP = 0.6 m

AK =2 AJ = 1.2 m

now, in Δ BNE

AJ = BE

angle ARJ = angle BNE = 60°

angle AJR = angle BNE = 60°

therefore,

ΔARJ ≈ ΔBNE

which shows,

RJ = NE

similarly Δ ALK ≈ Δ BMF

LK = MF

in Δ ARJ

tan 60° = AJ/KJ

√3 = 0.6/ KJ

KJ = 0.34

in Δ ALK

tan 60° = AK/LK

LK = 0.69

in Δ ACP

sin 60° = AP/AC

AC = 2.07

AC = BD = 2.07

we know

KN = RJ + EN + JE

KN = 2KJ + AB

KN = 2× 0.34 + 0.5

KN = 1.19

similarly

LM = 1.88

now,

length of each leg = 2.1

length of each step =RN = 1.2

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