Question

In triangle PQR, A and B are points on side QR such that they trisect QR. Prove that, ar( triangle PBR) = 0.5 ar( triangle PQB).

pls give the answer with steps...pls help me guys
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Answer 1

Explanation:

We assume the problem statement is telling us that the order of points on segment QR is Q, A, B, R, and that QA = AB = BR. This means that

  QB = QA +AB = 2BR

  BR = 1/2(QB)

The area of the triangles will be ...

  A = 1/2bh

For triangle PQB, the area is ...

  ar(PQB) = 1/2(QB)h . . . . . h is the perpendicular distance from QR to P

For triangle PBR, the area is ...

  ar(PBR) = 1/2(BR)h = 1/2(1/2QB)h . . . . h is the same as above

  ar(PBR) = 1/2ar(PQB)

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Essentially, you're showing the base of the smaller triangle is 1/2 the base of the larger one and using that to show the area of the smaller triangle is 1/2 the area of the larger one. (Both have the same height.)