Geometry Practice Test 4

Question : 33 of 40

Marks: +1, -0

In the figure given above, ABC is an equilateral triangle of side length 30 cm. XY is parallel to BC, XP is parallel to AC and YQ is parallel to AS.
If (XY + XP + YQ) is 40 cm, then what is PQ equal to?

5 cm
12 cm
15 cm
None of these

Validate

Solution:

AB = BC = AC = 30
XY + XP + YQ = 40

{BX}/{AB}

{XP}/{AC}

by using proportional theorem,
⇒ BX = XP

{AX}/{AB}

{XY}/{BC}

⇒ AX = XY

Similarly, YC = YQ
We have XY + XP × YQ = 40
BX + YC + AX = 40
⇒ YC = 10
So, YC = YQ = 10
BX = BP = 10
BP + PQ + QC = 30
10 + PQ + 10 = 30
PQ = 10

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