ДанотреугольникABCAC=21AB-BC=7Sabc=84Pabc=?. Created by Robka2000. geometriya-ru

ДанотреугольникABCAC=21AB-BC=...

Robka2000 @Robka2000

July 2022 1 5 Report

Дано
треугольникABC
AC=21
AB-BC=7
Sabc=84
Pabc=?

Answers & Comments

Удачник66

Verified answer

Можно попробовать найти площадь
AC = 21
AB = BC + 7
P = AB + BC + AC = BC + 7 + BC + 21 = 2BC + 28
p = P/2 = BC + 14
По формуле Герона
S = √[p*(p-AB)(p-AC)(p-BC)] = √[(BC+14)(BC+14-BC-7)(BC+14-21)(BC+14-BC)] =
= √[(BC+14)*7*(BC-7)*14] = 7*√[2*(BC+14)*(BC-7)] = 84
√[2*(BC+14)*(BC-7)] = 84/7 = 12
2*(BC+14)*(BC-7) = 12^2 = 144
(BC+14)*(BC-7) = 72
BC^2 + 7BC - 98 = 72
BC^2 + 7BC - 170 = 0
D= 7^2 + 4*170 = 49 + 680 = 729 = 27^2
BC = (-7 + 27)/2 = 10
AB = 17, AC = 21
P = AB + AC + BC = 10 + 17 + 21 = 48

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