{"id":1585,"date":"2025-12-31T12:45:20","date_gmt":"2025-12-31T11:45:20","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1585"},"modified":"2025-12-31T12:45:24","modified_gmt":"2025-12-31T11:45:24","slug":"zadanie-153","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1585","title":{"rendered":"Zadanie 153"},"content":{"rendered":"\n<p><strong>zadanie 32 &#8211; czerwiec 2021 (zadanie otwarte) (2pkt)<\/strong><\/p>\n\n\n\n<p>Dany jest trapez o podstawach d\u0142ugo\u015bci\u00a0<strong>a<\/strong>\u00a0oraz<strong>\u00a0b\u00a0<\/strong>i wysoko\u015bci\u00a0<strong>h<\/strong>. Ka\u017cd\u0105 z podstaw tego trapezu wyd\u0142u\u017cono o<strong>\u00a025%<\/strong>, a wysoko\u015b\u0107 skr\u00f3cono tak, \u017ce powsta\u0142 nowy trapez o takim samym polu. Oblicz, o ile procent skr\u00f3cono wysoko\u015b\u0107<strong>\u00a0h<\/strong>\u00a0trapezu.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n    <div class=\"premium-wrapper-odp\" id=\"odp_69e22b50282c8\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22b50282c8\"\n                style=\"margin-top:10px; padding:12px 20px; background:#28a745; color:#fff; border-radius:25px; border:none; cursor:pointer; font-weight:bold;\">\n            Poka\u017c odpowied\u017a\n        <\/button>\n\n        <div class=\"premium-content-odp\" style=\"display:none; padding:15px; border:1px solid #28a745; margin-top:10px; background:#e6ffe6; border-radius:25px;\">\n            \nPrawid\u0142owa odpowied\u017a to: Wysoko\u015b\u0107 trapezu skr\u00f3cono o 20%.\n        <\/div>\n    <\/div>\n    \n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n    <div class=\"premium-wrapper-wyjasnienie\" id=\"wyjasnienie_69e22b50282d4\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22b50282d4\"\n                style=\"margin-top:10px; padding:12px 20px; background:#28a745; color:#fff; border-radius:25px; border:none; cursor:pointer; font-weight:bold;\">\n            Poka\u017c wyja\u015bnienie\n        <\/button>\n\n        <div class=\"premium-content-wyjasnienie\" style=\"display:none; padding:15px; border:1px solid #28a745; margin-top:10px; background:#e6ffe6; border-radius:25px;\">\n            \n<h2>Wyja\u015bnienie<\/h2>\n\n<p>Pole trapezu o podstawach <code>a<\/code> i <code>b<\/code> oraz wysoko\u015bci <code>h<\/code> wynosi:<\/p>\n\n<p><code>P = ((a + b) \/ 2) \u00b7 h<\/code><\/p>\n\n<h3>Krok 1: Zmiana podstaw<\/h3>\n\n<p>Ka\u017cd\u0105 z podstaw zwi\u0119kszono o 25%, wi\u0119c nowe podstawy maj\u0105 d\u0142ugo\u015bci:<\/p>\n\n<p><code>1.25a<\/code> oraz <code>1.25b<\/code><\/p>\n\n<p>Suma nowych podstaw:<\/p>\n\n<p><code>1.25a + 1.25b = 1.25(a + b)<\/code><\/p>\n\n<h3>Krok 2: Nowe pole trapezu<\/h3>\n\n<p>Nowe pole ma by\u0107 takie samo jak stare, wi\u0119c:<\/p>\n\n<p>\n<code>((1.25(a + b)) \/ 2) \u00b7 h<sub>new<\/sub> = ((a + b) \/ 2) \u00b7 h<\/code>\n<\/p>\n\n<h3>Krok 3: Wyznaczenie nowej wysoko\u015bci<\/h3>\n\n<p>Dzielimy obie strony r\u00f3wnania przez <code>((a + b)\/2)<\/code>:<\/p>\n\n<p>\n<code>1.25 \u00b7 h<sub>new<\/sub> = h<\/code>\n<\/p>\n\n<p>St\u0105d:<\/p>\n\n<p>\n<code>h<sub>new<\/sub> = h \/ 1.25 = 0.8h<\/code>\n<\/p>\n\n<h3>Krok 4: O ile procent skr\u00f3cono wysoko\u015b\u0107?<\/h3>\n\n<p>Nowa wysoko\u015b\u0107 to <strong>80%<\/strong> starej wysoko\u015bci.<\/p>\n\n<p>Oznacza to skr\u00f3cenie o:<\/p>\n\n<p><strong>100% \u2212 80% = 20%<\/strong><\/p>\n\n<h3>Wniosek<\/h3>\n\n<p>Wysoko\u015b\u0107 trapezu skr\u00f3cono o <strong>20%<\/strong>.<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 32 &#8211; czerwiec 2021 (zadanie otwarte) (2pkt) Dany jest trapez o podstawach d\u0142ugo\u015bci\u00a0a\u00a0oraz\u00a0b\u00a0i wysoko\u015bci\u00a0h. Ka\u017cd\u0105 z podstaw tego trapezu wyd\u0142u\u017cono o\u00a025%, a wysoko\u015b\u0107 skr\u00f3cono tak, \u017ce powsta\u0142 nowy trapez o takim samym polu. Oblicz, o ile procent skr\u00f3cono wysoko\u015b\u0107\u00a0h\u00a0trapezu.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"saved_in_kubio":false,"_uag_custom_page_level_css":"","_themeisle_gutenberg_block_has_review":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[25,36,204,81,83],"tags":[23,35,205],"class_list":["post-1585","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-czerwiec-2021","category-rozne","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-czerwiec-2021","tag-rozne"],"jetpack_featured_media_url":"","uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false,"kubio-fullhd":false,"woocommerce_thumbnail":false,"woocommerce_single":false,"woocommerce_gallery_thumbnail":false},"uagb_author_info":{"display_name":"adminmymatma","author_link":"https:\/\/mymatma.pl\/?author=1"},"uagb_comment_info":0,"uagb_excerpt":"zadanie 32 &#8211; czerwiec 2021 (zadanie otwarte) (2pkt) Dany jest trapez o podstawach d\u0142ugo\u015bci\u00a0a\u00a0oraz\u00a0b\u00a0i wysoko\u015bci\u00a0h. Ka\u017cd\u0105 z podstaw tego trapezu wyd\u0142u\u017cono o\u00a025%, a wysoko\u015b\u0107 skr\u00f3cono tak, \u017ce powsta\u0142 nowy trapez o takim samym polu. Oblicz, o ile procent skr\u00f3cono wysoko\u015b\u0107\u00a0h\u00a0trapezu.","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1585","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1585"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1585\/revisions"}],"predecessor-version":[{"id":1588,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1585\/revisions\/1588"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1585"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1585"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1585"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}