Bonjour svp j’aurais besoin d’aide pour l’exercice 2 svp.... Pergunta de ideia deStukira

May 2019 1 135 Report

Bonjour svp j’aurais besoin d’aide pour l’exercice 2 svp

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trudelmichel Bonjour,
EF=EB+BF=2a+1/2a=5/2a
triangle rectangleCBE
CE²=CB²+BC²
CE²=a²+(2a)²=a²+4²=5a²
CE=√5a²=a√5

triangle FBC
CF²=BC²+FB²
CF²=a²+(1/2a)²=a²+1/4a²=5/4a²
CF=√5/4a²
CF=1/2a√5

A(0,0) B(a,0) C(a.a) D'0,a)
AE=AB+BE=a+2a=3a
E(3a;0)
AF=1/2AB=1/2a
F(1/2a, 0)

EF²=(xf-xe)²+(yf-ye)²
EF²= (1/2a-3a)²+(0-0)²
EF²=(1/2a-6/2a)²
EF²=(-5/2a)²
EF²=25/4a²
EF=√25/4 a²
EF=5/2a

CE²=(xe-xc)²+(ye-yc)²
CE²=(3a-a)²+(0-a)²
CE²=(2a)²+(-a)²
CE²=4a²-a²
CE²=5a²
CE=√5a²
CE=a√5

CF²=(xf-xc)²+(yf-yc)²
CF²=(1/2a-a)²+(0-a)²
CF²=(-1/2a)²+(-a)²
CF²= 1/4a²+a²
CF²=5/4a²
CF=√5/4a²
CF=1/2a√5

je remarque que
5a²+5/4a²=20/4a²+5/4a²=25/4a²
d'où
EF²=CE²+CF²
caractéristique d'un triangle rectangle en C

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