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Question
If ΔABC ∼ ΔDEF, length of side AB is 9 cm and length of side DE is 12 cm, then find the ratio of their corresponding areas.
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Solution
Given: ΔABC ∼ ΔDEF
Also, AB = 9 cm, DE = 12 cm.
We now know the area theorem of comparable triangles.
`(ar(ΔABC))/(ar(ΔDEF)) = ((AB)/(DE))^2` ...(i)
Substituting the values in equation (i),
`(ar(ΔABC))/(ar(ΔDEF)) = (9/12)^2`
= `(3/4)^2`
= `9/16`
Hence, the ratio of areas of ΔABC and ΔDEF is 9:16.
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