I gimnazjum

Matematyka wokół nas 1

a)&nbsp; h2=42−(21​⋅4)2 h2=16−4 h2=12 h=12<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>​[cm] P=21​⋅4⋅12<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>​=212<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>​[cm2]

d2=1,52+1,52 d2=2,25+2,25

<img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/25299/ojCropxC/ouvdgTsH9VM0w%3D%3D_3ce2cf0021d7e6ecb96780fd708cdc4aadb620aa136bf3991c5ec7105e7e5f67.jpg" width="233" height="233"> &nbsp; r2=122+92

a) a2=152−122 a2=225−144 a2=81 a=9[cm] &nbsp; r=29​=4,5[cm]

a - długość prostokąta 0,75a &nbsp;- szerokość prostokąta&nbsp; &nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; d2=42+32 d

<img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/24987/VNWaTYbmvHZkdmeGkjyilA%3D%3D_f48dfe6fed5c55ce03afd3c4197cb872ffe3b4fcb93db5e14d2989fa7b25639b.jpg" width="197" height="148"> (32​a)2+(21​a)2=152

<img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/25000/%2BXESAioM9w7NnhKKjp84mA%3D%3D_4af08ada35f6507db82d7a36195b86fa596d9436395be06091fcd35db2d87ef0.jpg" width="332" height="198"> &nbsp; ∣AE∣=∣DC∣=20cm ∣EB∣=8cm ∣AB∣=20+8=28cm

<img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/25379/a15mLp83fqkbDf079s4GkQ%3D%3D_88dcb46019c5979d99b2c528a19bd89410670995fe8d9c3eedafec9748cb69f3.jpg" width="335" height="322"> &nbsp; &nbsp; ∣AC∣=5 &nbsp; ∣BC∣=6 &nbsp; &nbsp; a)

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