If ΔABC ~ ΔDEF such that BC = 4.5 cm and EF = 3.5 cm and ar(ΔABC) = 81 cm2, then ar(ΔDEF) = 64 cm2.TrueFalse
Question
If ΔABC ~ ΔDEF such that BC = 4.5 cm and EF = 3.5 cm and ar(ΔABC) = 81 cm2, then ar(ΔDEF) = 64 cm2.TrueFalse
Solution
False.
The areas of similar triangles are proportional to the square of the ratio of their corresponding sides.
Given that ΔABC ~ ΔDEF, the ratio of their sides is BC/EF = 4.5/3.5 = 1.2857 (approximately).
So, the ratio of their areas should be (BC/EF)^2 = 1.2857^2 = 1.65306122449 (approximately).
Given that the area of ΔABC is 81 cm^2, the area of ΔDEF should be 81/1.65306122449 = 49 cm^2 (approximately), not 64 cm^2.
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