Question

In ΔABC , PQ is a line segment intersecting AB at P and AC at Q such that PQ||BC and PQ divides ΔABC into two parts equal in area. Find BP / AB .

Answer 1

Answer:

From the attached figure below, the value of BP / AB is ($\sqrt{2$ - 1) / $\sqrt{2}$

Step-by-step explanation:

• Let the area of the triangle Δ ABC is 2 unit.

• Line PQ divides the area of Δ ABC into two equal parts.

• ∴ the area of Δ APQ is = 1 unit.

• ∵ line PQ is parallel to the line BC, and Angle A is common in both the triangle.

∴ Δ APQ ≅ Δ ABC       (similar)

• ∴$\dfrac{area ABC}{area APQ}$  = $\dfrac{AB^{2}}{AP^{2}}$            (according to the similarity Property)

•               $\dfrac{2}{1}$   = $\dfrac{AB^{2}}{AP^{2}}$

•              $\dfrac{AP}{AB}$  = $\dfrac{1}{\sqrt{2} }$

•     $\dfrac{AB -BP}{AB}$ = $\dfrac{1}{\sqrt{2} }$           (∵ AB = AP + BP)

∴       $\dfrac{BP}{AB }$    = $\dfrac{\sqrt{2}-1 }{\sqrt{2} }$