UPSC CDS 2 2018 Math Paper

ΔABC is an equilateral triangle with each side = 30 cm.Since PX || AC
∴ ∠BXP =∠ XPB =60°
Also XBP = 60°
Let PX be x
Then BP = x and BX = x
Similarly,
YQ = QC = YC = x
Also in Δ AXY :
AX=XY=AY=(30−x)cm
Now,
It is given that XY + XP + YQ = 40
∴30−x+2x=40
⇒x=10cm
PQ=30–2x=30–2×10=10cm