If the ratio of altitudes of two triangles are m and n and having equal bases, then the ratio of their areas is equal to
A
m2:n2
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B
m:n
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C
1m2:1n2
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D
2m2:3n2
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Solution
The correct option is B m:n Let the two triangles be ΔABCandΔPQR with their altitudes be AD and PS respectively. Ar(ΔABC)=12×BC×ADAr(ΔPQR)=12×QR×PS∴Ar(ΔABC)Ar(ΔPQR)=12×BC×AD12×QR×PS=BCQR×ADPS=ADPS(∵BC=QR)=mn(∵ADDS=mn)