In the figure , BC=2/5AB, AC=20cm. find the area of △ABC.
(correct your answer to 3 significant figures)
http://img29.imageshack.us/img29/8353/20100715.jpg
pythagoras's theroem (s2)
2010-07-15 6:09 pm
回答 (1)
2010-07-16 12:32 am
✔ 最佳答案
AB^2 + BC^2 = 20^2AB^2 + [(2/5)AB]^2 = 400AB^2 + (4/25)AB^2 = 400(1 + 4/25) AB^2 = 400(29/25) AB^2 = 400AB^2 = 10000 / 29AB = 100 / √29AB = 100√29 / 29So BC = (2/5)(100√29 / 29)= 40√29 / 29the area of △ABC= (1/2) AB BC= (1/2) (100√29 / 29) (40√29 / 29)= 100 * 40 * √29 * √29 / (2 * 29 * 29)= 2000 / 29= 68.9655...= 69.0 cm^2 (3 significant figures)
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