{"id":679355,"date":"2023-09-03T03:11:14","date_gmt":"2023-09-02T21:41:14","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/in-the-figure-given-above-if-de-%e2%88%a5bc-then-the-value-of-x-equals-to\/"},"modified":"2025-06-20T13:23:40","modified_gmt":"2025-06-20T07:53:40","slug":"in-the-figure-given-above-if-de-%e2%88%a5bc-then-the-value-of-x-equals-to","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/in-the-figure-given-above-if-de-bc-then-the-value-of-x-eq\/","title":{"rendered":"In the figure given above, if DE \u2225BC, then the value of x equals to"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"In the figure given above, if DE \u2225BC, then the value of x equals to","custom_permalink":"question\/mathematics\/in-the-figure-given-above-if-de-bc-then-the-value-of-x-eq\/"},"categories":[],"acf":{"question":"

\"\"<\/p>

In the figure given above, if DE <\/span>\u2225<\/mo><\/math>BC, then the value of x equals to<\/span><\/p>

<\/p>

<\/p><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal;font-size:12pt\"><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal;font-size:12pt\">","options":[{"option":"    <\/span>3 cm<\/span>","correct":false},{"option":"    <\/span>2 cm<\/span>","correct":false},{"option":"    <\/span>4 cm<\/span>","correct":false},{"option":"    <\/span>6.7 cm<\/span> <\/span>","correct":true}],"solution":"Given that DE <\/span>\u2225<\/mo><\/math>BC.<\/span>
\"\"In <\/span>\u25b3<\/mo>ADE<\/mi><\/math>and <\/span>\u25b3<\/mo>ABC<\/mi><\/math>, <\/span>
\u2220<\/mo>ADE<\/mi>=<\/mo>\u2220<\/mo>ABC<\/mi><\/math>(As <\/span>DE<\/mi>\u2225<\/mo>BC<\/mi><\/math>) (Corresponding angles are equal) <\/span>
 <\/span>\u2220<\/mo>AED<\/mi>=<\/mo>\u2220<\/mo>ACB<\/mi><\/math>(As <\/span>DE<\/mi>\u2225<\/mo>BC<\/mi><\/math>) (Corresponding angles are equal) <\/span>
\u2220<\/mo>DAE<\/mi>=<\/mo>\u2220<\/mo>BAC<\/mi><\/math> (common angle) <\/span>
\u25b3<\/mo>ADE<\/mi>~<\/mo>\u25b3<\/mo>ABC<\/mi><\/math> (By AAA rule)<\/span>
Now, if two triangles are similar, then their corresponding sides are proportional. <\/span>
AD<\/mi><\/mrow>AB<\/mi><\/mrow><\/mfrac>=<\/mo>DE<\/mi><\/mrow>BC<\/mi><\/mrow><\/mfrac><\/math> <\/span>\u21d2<\/mo>3<\/mn><\/mrow>2<\/mn>+<\/mo>3<\/mn><\/mrow><\/mfrac>=<\/mo>4<\/mn><\/mrow>x<\/mi><\/mrow><\/mfrac><\/math> <\/span>\u21d2<\/mo>x<\/mi>=<\/mo>6<\/mn>.<\/mo>7<\/mn>cm<\/mi><\/math>.<\/span>
Therefore, the value of <\/span>x is <\/mi>6<\/mn>.<\/mo>7<\/mn>cm<\/mi><\/math>.<\/span>
Hence option 4 is the answer.<\/span>
 <\/span>","subject":"Mathematics"},"yoast_head":"\nIn the figure given above, if DE \u2225BC, then the value of x equals to - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"In the figure given above, if DE \u2225BC, then the value of x equals to\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/in-the-figure-given-above-if-de-bc-then-the-value-of-x-eq\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"In the figure given above, if DE \u2225BC, then the value of x equals to - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\"In the figure given above, if DE \u2225BC, then the value of x equals to\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/in-the-figure-given-above-if-de-bc-then-the-value-of-x-eq\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:modified_time\" content=\"2025-06-20T07:53:40+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1008\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"In the figure given above, if DE \u2225BC, then the value of x equals to - 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