Mathematics
BP and CQ are two medians of a △ABC. If QP = 4 cm, then BC =
2 cm
6 cm
8 cm
9 cm
Mid-point Theorem
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Answer
Given,
BP is the median.
∴ P is the mid-point of AC
CQ is the median.
∴ Q is the mid-point of AB
By mid-point theorem,
The line segment joining the mid points of any two sides of a triangle is parallel to the third side and is equal to half of it.
Since, Q and P are the mid-points of AB and AC respectively. Thus,
⇒ QP || BC and QP = BC
⇒ BC = 2 × QP
⇒ BC = 2 × 4
⇒ BC = 8 cm.
Hence, option 3 is the correct option.
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