In the diagram given below, ∠ABD = ∠CDB = ∠PQD = 90°. If AB : CD = 3 : 1, the ratio of CD : PQ is
Explanation:
Consider the figure below,
As AB || CD and ∠ABD = ∠CDB = ∠PQD = 90°
∴ ∠BAP = ∠CDP and ∠ABP = ∠DCP
∆CPD ~ ∆BPA …(AAA test)
∴CPPB=x3x=13
If CP = y,
PB = 3y
Now, ∆CBD ~ ∆PBQ …(AA test)
CDPQ=CBPB=y+3y3y=43= 1 : 0.75
Hence, option (b).
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