In triangle pqr a and b are points on side qr such that they trisect qr. Prove that at(pqb)=at(pbr)
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Given PQR is a triangle & A & B are points on OR such that OA=AB=BR
Therefore to prove area ΔPQB=area ΔPOQ+ΔPBR(area)
AreaΔPQA=1/2×QA×h=1/2×1/3QR×h.............(i)
Area ΔPQB=1/2×QB×h=1/2×2/3QR×h............(ii)
Area ΔPBR=1/2×BR×h=1/2×1/3QR×h...............(iii)
Therefore area ΔPQB=area of ΔPQA×area ofΔPBR
Therefore to prove area ΔPQB=area ΔPOQ+ΔPBR(area)
AreaΔPQA=1/2×QA×h=1/2×1/3QR×h.............(i)
Area ΔPQB=1/2×QB×h=1/2×2/3QR×h............(ii)
Area ΔPBR=1/2×BR×h=1/2×1/3QR×h...............(iii)
Therefore area ΔPQB=area of ΔPQA×area ofΔPBR
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