.In figure, MN ǁ QR, and PM: MQ = 8: 5. Find
area of ∆QOR/area of ∆MON
Answers
Given : MN ǁ QR, and PM: MQ = 8: 5
To find : area of ∆QOR/area of ∆MON
Solution:
MN ǁ QR
=> Δ PMN ≈ Δ PQR
=> PM/PQ = MN/QR
=> PM/(PM + MQ) = MN/QR
=> 8/(8 + 5) = MN/QR
=> MN/QR = 8/13
in Δ MON & Δ ROQ
∠OMN = ∠ORQ
∠ONM = ∠OQR
∠MON = ∠ROQ
=> Δ MON ≈ Δ ROQ
Area of Δ MON / Area of Δ ROQ = (MN/ QR)²
=> Area of Δ MON / Area of Δ QOR = (8/ 13)²
=> Area of Δ MON / Area of Δ QOR = 64/169
=> Area of Δ QOR/Area of Δ MON = 169/64
Area of Δ QOR/Area of Δ MON = 169/64
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Answer:
Step-by-step explanation:
Given : MN ǁ QR, and PM: MQ = 8: 5
To find : area of ∆QOR/area of ∆MON
Solution:
MN ǁ QR
=> Δ PMN ≈ Δ PQR
=> PM/PQ = MN/QR
=> PM/(PM + MQ) = MN/QR
=> 8/(8 + 5) = MN/QR
=> MN/QR = 8/13
in Δ MON & Δ ROQ
∠OMN = ∠ORQ
∠ONM = ∠OQR
∠MON = ∠ROQ
=> Δ MON ≈ Δ ROQ
Area of Δ MON / Area of Δ ROQ = (MN/ QR)²
=> Area of Δ MON / Area of Δ QOR = (8/ 13)²
=> Area of Δ MON / Area of Δ QOR = 64/169
=> Area of Δ QOR/Area of Δ MON = 169/64
Area of Δ QOR/Area of Δ MON = 169/64