S = pr, где p = 0,5(AB + BC + AC) = 0,5(17x + 17x + 24x) = 29x.
По формуле Герона S =√(p(p - AB)(p - BC)(p - AC)) =
=√(29x(29x - 17x)(29x - 17x)(29x - 24x)) = √(29x∙12x∙12x∙5x) = 12√(145)x².
Имеем, 12√(145)x² = 1680; √(145)x² = 140; x² = 140/√(145) = 140√(145)/145 =
= 28√(145)/29; x = √(28√(145)/29) = 2√(7√(145)/29).
p = 29∙2√(7√(145)/29) = 2√(29∙7√(145)) = 2√(203√(145)) (см).
r = S/p = 1680/2√(203√(145)) = 840/√(203√(145))(см).
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S = pr, где p = 0,5(AB + BC + AC) = 0,5(17x + 17x + 24x) = 29x.
По формуле Герона S =√(p(p - AB)(p - BC)(p - AC)) =
=√(29x(29x - 17x)(29x - 17x)(29x - 24x)) = √(29x∙12x∙12x∙5x) = 12√(145)x².
Имеем, 12√(145)x² = 1680; √(145)x² = 140; x² = 140/√(145) = 140√(145)/145 =
= 28√(145)/29; x = √(28√(145)/29) = 2√(7√(145)/29).
p = 29∙2√(7√(145)/29) = 2√(29∙7√(145)) = 2√(203√(145)) (см).
r = S/p = 1680/2√(203√(145)) = 840/√(203√(145))(см).