{"id":26276,"date":"2025-06-19T11:50:26","date_gmt":"2025-06-19T11:50:26","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=26276"},"modified":"2025-06-19T11:50:28","modified_gmt":"2025-06-19T11:50:28","slug":"determine-whether-a-triangle-with-the-given-side-lengths-is-a-right-triangle-side-lengths-right-triangle-not-a-right-triangle-not-enough-information-8-15-17-6-7-9-18-32-40-10-24-26","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/determine-whether-a-triangle-with-the-given-side-lengths-is-a-right-triangle-side-lengths-right-triangle-not-a-right-triangle-not-enough-information-8-15-17-6-7-9-18-32-40-10-24-26\/","title":{"rendered":"Determine whether a triangle with the given side lengths is a right triangle Side lengths Right triangle Not a right triangle Not enough information 8, 15, 17 6, 7, 9 18, 32, 40 10, 24, 26"},"content":{"rendered":"\n<p>Determine whether a triangle with the given side lengths is a right triangle Side lengths Right triangle Not a right triangle Not enough information 8, 15, 17 6, 7, 9 18, 32, 40 10, 24, 26<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-green-cyan-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To determine whether a triangle is a <strong>right triangle<\/strong>, we use the <strong>Pythagorean Theorem<\/strong>, which states that for a triangle with side lengths aaa, bbb, and ccc, where ccc is the longest side, the triangle is a right triangle if:a2+b2=c2a^2 + b^2 = c^2a2+b2=c2<\/p>\n\n\n\n<p>Let us evaluate each set of side lengths:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>1. 8, 15, 17<\/strong><\/p>\n\n\n\n<p>Here, 17 is the longest side.82+152=64+225=2898^2 + 15^2 = 64 + 225 = 28982+152=64+225=289172=28917^2 = 289172=289<\/p>\n\n\n\n<p>Since both values are equal, this <strong>is a right triangle<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>2. 6, 7, 9<\/strong><\/p>\n\n\n\n<p>Here, 9 is the longest side.62+72=36+49=856^2 + 7^2 = 36 + 49 = 8562+72=36+49=8592=819^2 = 8192=81<\/p>\n\n\n\n<p>Since 85 \u2260 81, this is <strong>not a right triangle<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>3. 18, 32, 40<\/strong><\/p>\n\n\n\n<p>Here, 40 is the longest side.182+322=324+1024=134818^2 + 32^2 = 324 + 1024 = 1348182+322=324+1024=1348402=160040^2 = 1600402=1600<\/p>\n\n\n\n<p>Since 1348 \u2260 1600, this is <strong>not a right triangle<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>4. 10, 24, 26<\/strong><\/p>\n\n\n\n<p>Here, 26 is the longest side.102+242=100+576=67610^2 + 24^2 = 100 + 576 = 676102+242=100+576=676262=67626^2 = 676262=676<\/p>\n\n\n\n<p>Since both values are equal, this <strong>is a right triangle<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Summary:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>8, 15, 17 \u2192 <strong>Right triangle<\/strong><\/li>\n\n\n\n<li>6, 7, 9 \u2192 <strong>Not a right triangle<\/strong><\/li>\n\n\n\n<li>18, 32, 40 \u2192 <strong>Not a right triangle<\/strong><\/li>\n\n\n\n<li>10, 24, 26 \u2192 <strong>Right triangle<\/strong><\/li>\n<\/ul>\n\n\n\n<p>The Pythagorean Theorem allows us to check for a right triangle by verifying whether the sum of the squares of the two shorter sides equals the square of the longest side. No additional information is needed when all three side lengths are provided.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"722\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-86.jpeg\" alt=\"\" class=\"wp-image-26277\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-86.jpeg 722w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-86-212x300.jpeg 212w\" sizes=\"auto, (max-width: 722px) 100vw, 722px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Determine whether a triangle with the given side lengths is a right triangle Side lengths Right triangle Not a right triangle Not enough information 8, 15, 17 6, 7, 9 18, 32, 40 10, 24, 26 The Correct Answer and Explanation is: To determine whether a triangle is a right triangle, we use the Pythagorean [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-26276","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26276","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=26276"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26276\/revisions"}],"predecessor-version":[{"id":26278,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26276\/revisions\/26278"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=26276"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=26276"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=26276"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}