In the figure given below ABC is an equilateral triangle with each side of length 30 cm XY is parall...........

Quantitative Aptitude (CDS) Mensuration 2D

In the figure given below, ABC is an equilateral triangle with each side of length 30 cm. XY is parallel to BC, XP is parallel to AC and YQ is parallel to AB. If XY + XP + YQ is 40 cm, then the value of PQ is

5 cm

12 cm

15 cm

10 cm

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Explanation:

In the given figure XY II BC
$\angle$ AXY = $\angle$ ABC ( Corresponding angles)
$\angle$ AYX = $\angle$ ACB ( Corresponding angles)
$\Delta$ AXY is also an equilateral triangle
XY + XP + YQ = 40
AX + XB + YQ = 40
30 + YQ = 40
YQ = 10 = QC
Similarly, XP = 10 = BP
BC = BP + PQ + QC
30 = 10 + PQ + 10
PQ = 10