III gimnazjum

Matematyka wokół nas 3

niech O będzie punktem przecięcia odcinka CD i EF ∣AB∣∣EF∣​=∣CD∣∣CO∣​ 9∣EF∣​=64​ 6∣EF∣=36 |EF|=6 Odp. Długość odcinka EF wynosi 6 cm.

Rozwiązanie 1

<img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/24162/Ni6RytFsu8ZCkW/vlc/H3g%3D%3D_b1a16497d0fe87f3d512b39df4a35ed5502ff3d08300fac1e1e9c1cd24460168.jpg" width="640" height="447"> ∇ABC∼   ~ ∇EBG                    (KKK) 9,6−3,29,6​=∣EG∣5,4​

Przyjmijmy oznaczenia jak na poniższym rysunku.  h - wysokość powstałego trójkąta  x - wysokość powstałego trapezu  <img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/24166/uYe2WmiHZKhr8YZDBBcAtg%3D%3D_83cfd775434480e8bb2fc2e401990c7af3d812a17ac80a7107968cedc20547a6.jpg" width="614" height="480"> h+x=4,8   3,5h​=64,8​

a=52−42<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.28em' viewBox='0 0 400000 1296' preserveAspectRatio='xMinYMin slice'><path d='M263,681c0.7,0,18,39.7,52,119
c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120
c340,-704.7,510.7,-1060.3,512,-1067
l0 -0
c4.7,-7.3,11,-11,19,-11
H40000v40H1012.3
s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232
c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1
s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26
c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z
M1001 80h400000v40h-400000z'/></svg>​ a=9<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​

2m = 200cm r = 100cm P=1002⋅Π

<img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/64992/17WqJs7I9C9WojDLt0wBZw%3D%3D_ad8eb22a7e5de74413d7ae134676360baae09728f84a202a9fcfac233787620b.jpg" width="560" height="480"> ∇ BCF~ ∇

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