A) 5 cm
B) 12 cm
C) 15 cm
D) 10 cm
Correct Answer: D
Solution :
Since, XP||AC, YQ||AB |
\[\therefore \] \[\angle XBP=\angle YQC\] and \[\angle XPB=\angle YCQ\] |
\[\therefore \]\[\Delta XBP\]and \[\Delta YCQ\]are equilateral triangles. |
Now, XY|| BC |
\[\therefore \] \[\frac{AX}{AB}=\frac{XY}{BC}\] |
\[\Rightarrow \] \[AX=XY\] \[(\because AB=BC=30\,\,\text{cm})\] |
Also, \[XY+XP+YQ=40\] |
\[\Rightarrow \]\[AX+XB+YQ=40\] \[(\because XY=AX,XP=XB)\] |
\[\Rightarrow \] \[AB+YQ=40\] |
\[\Rightarrow \] \[YQ=40-30=10\,\,\text{cm}\] |
\[\therefore \] \[YQ=XP=10\,\,\text{cm}\] |
\[\therefore \] \[BP=CQ=10\,\,\text{cm}\] |
\[\therefore \] \[PQ=30-BP-CQ=30-10-10=10\,\,\text{cm}\] |
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