II gimnazjum

Matematyka z plusem 2

Liczymy z tw. Pitagorasa x2=42+82=16+64=80 x=80<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
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M834 80h400000v40h-400000z'/></svg>​=16⋅5<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
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M834 80h400000v40h-400000z'/></svg>​=45<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
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M834 80h400000v40h-400000z'/></svg>​ Odpowiedź A<section class="answer"><h4 class="answer-heading">Odpowiedź:</h4> A</section>

Rozwiązanie 1

Liczymy z tw. Pitagorasa (23<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
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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>​)2=a2+22

Liczymy z tw. Pitagorasa 102=72+x2

Trójkąt ABC jest prostokątny, ponieważ kąt ACB jest prosty (kąt wpisany w koło, oparty na tym samym łuku co średnica), mamy 42=∣AC∣2+12

Przekątna prostokąta dzieli go na dwa trójkąty prostokątne. Zatem długość drugiego boku prostokąta liczymy z tw. Pitagorasa 62=22+x2

52=32+h2 h2=25−9=16

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