III gimnazjum

Matematyka wokół nas 3

Skala podobieństwa mniejszego półokręgu do większego wynosi: 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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Rozwiązanie 1

Podobienˊstwo figur oznacza zachowanie stałych proporcji wszystkich bokoˊw, tzn. tej samej skali podobienˊstwa.

Boki prostokąta są w proporcji 2:4. Oznacza to, z˙e szukamy takiego prostokąta podobnego, ktoˊry ma długosˊci bokoˊw roˊwne:

Trapezy prostokątne opisane w zadaniu mają te same kąty (90o, 90o, 135o, 45o).

Wystarczy pomnoz˙ycˊ długosˊcˊ obwodu na mapie przez mianownik skali:

Skala podobienˊstwa wynosi:

Trapez ABCD ma wysokosˊcˊ (oznaczmy jako h) stanowiącą 120% długosˊci kroˊtszej podstawy, czyli: h=1,2⋅18 cm=18+3,6=21,6 cm

Musimy skorzystać z tw. Pitagorasa i policzyć brakujące długości boków. Trójkąt o przyprostokątnej 4 cm i przeciwprostokątnej 5cm ma drugą przyprostokątną (x) równą: x2+42=52 x=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
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Najwygodniejszy sposób nauki z edukacyjnym Odrabiamy AI

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