{"id":35900,"date":"2025-06-24T18:10:29","date_gmt":"2025-06-24T18:10:29","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=35900"},"modified":"2025-06-24T18:10:30","modified_gmt":"2025-06-24T18:10:30","slug":"which-of-the-following-possibilities-will-form-a-triangle-2","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/which-of-the-following-possibilities-will-form-a-triangle-2\/","title":{"rendered":"Which of the following possibilities will form a triangle"},"content":{"rendered":"\n<p>Which of the following possibilities will form a triangle? A: Side = 15 cm, side = 7 cm, side = 7 cm B: Side = 15 cm, side = 7 cm, side = 9 cm C: Side = 14 cm, side = 6 cm, side = 7 cm D: Side = 14 cm, side = 6 cm, side = 8 cm<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer: C and D<\/strong><\/p>\n\n\n\n<p>To determine which sets of side lengths can form a triangle, we use the <strong>triangle inequality theorem<\/strong>. This theorem states that for any three sides to form a triangle, <strong>the sum of the lengths of any two sides must be greater than the length of the third side<\/strong>.<\/p>\n\n\n\n<p>Let&#8217;s test each option:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>A: 15 cm, 7 cm, 7 cm<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>15 + 7 = 22 > 7 \u2714<\/li>\n\n\n\n<li>15 + 7 = 22 > 7 \u2714<\/li>\n\n\n\n<li>7 + 7 = 14 &lt; 15 \u2718<br>Since one pair fails the triangle inequality, this cannot form a triangle.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>B: 15 cm, 7 cm, 9 cm<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>15 + 7 = 22 > 9 \u2714<\/li>\n\n\n\n<li>15 + 9 = 24 > 7 \u2714<\/li>\n\n\n\n<li>7 + 9 = 16 > 15 \u2714<br>All conditions are satisfied, so at first glance, this seems correct. However, we must re-express and double-check.<br>Actually:<\/li>\n\n\n\n<li>7 + 9 = 16<\/li>\n\n\n\n<li>16 is <em>just<\/em> greater than 15<br>So it does form a triangle.<br>Correction: <strong>B is valid<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>C: 14 cm, 6 cm, 7 cm<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>14 + 6 = 20 > 7 \u2714<\/li>\n\n\n\n<li>14 + 7 = 21 > 6 \u2714<\/li>\n\n\n\n<li>6 + 7 = 13 &lt; 14 \u2718<br>One condition fails, so <strong>C is invalid<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>D: 14 cm, 6 cm, 8 cm<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>14 + 6 = 20 > 8 \u2714<\/li>\n\n\n\n<li>14 + 8 = 22 > 6 \u2714<\/li>\n\n\n\n<li>6 + 8 = 14 \u2714 (equal but not less)<br>All conditions are either greater or equal but not failing. Hence, <strong>D is valid<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Final Conclusion<\/strong>: The sets that can form a triangle are <strong>B and D<\/strong>.<\/p>\n\n\n\n<p>Now let&#8217;s explain the concept:<\/p>\n\n\n\n<p>A triangle is a closed figure with three sides. For any three segments to form a triangle, their lengths must satisfy the triangle inequality rule. The key idea is that no single side should be as long as or longer than the sum of the other two. If that happens, the figure will not close to form a triangle. This ensures that the sides can physically connect in space to form a triangle. In our case, only options B and D met all the necessary conditions.<\/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-banner10-345.jpeg\" alt=\"\" class=\"wp-image-35901\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-345.jpeg 722w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-345-212x300.jpeg 212w\" sizes=\"auto, (max-width: 722px) 100vw, 722px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Which of the following possibilities will form a triangle? A: Side = 15 cm, side = 7 cm, side = 7 cm B: Side = 15 cm, side = 7 cm, side = 9 cm C: Side = 14 cm, side = 6 cm, side = 7 cm D: Side = 14 cm, side = [&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-35900","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35900","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=35900"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35900\/revisions"}],"predecessor-version":[{"id":35902,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35900\/revisions\/35902"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=35900"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=35900"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=35900"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}