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Sagot :
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.)
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