{"id":225,"date":"2020-01-15T12:01:08","date_gmt":"2020-01-15T12:01:08","guid":{"rendered":"http:\/\/mathfun4kids.com\/mlog\/?p=225"},"modified":"2020-10-13T12:30:22","modified_gmt":"2020-10-13T12:30:22","slug":"mathcount-exercises-12","status":"publish","type":"post","link":"https:\/\/mathfun4kids.com\/mlog\/?p=225","title":{"rendered":"MATHCOUNTS Exercises &#8211; 12"},"content":{"rendered":"\n<p>In $\\triangle{ABC}$, $\\overline{AB}=5$, $\\overline{AC}=6$, $\\overline{BC}=7$. Square $BCED$ is drawn along the side of $\\overline{BC}$, as shown in the following figure. Find the area of $\\triangle{ADE}$. <a href=\"javascript:toggle_visibility('sol-mathcounts-exercises-12');toggle_visibility('img-mathcounts-exercises-12');\">Click here for the hint.<\/a><\/p>\n\n\n\n<div id=\"img-mathcounts-exercises-12\" style=\"display:block\" class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" src=\"https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2020\/10\/Screen-Shot-2020-01-14-at-10.05.13-AM.png\" alt=\"\" class=\"wp-image-226\" width=\"208\" height=\"268\" srcset=\"https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2020\/10\/Screen-Shot-2020-01-14-at-10.05.13-AM.png 416w, https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2020\/10\/Screen-Shot-2020-01-14-at-10.05.13-AM-233x300.png 233w\" sizes=\"(max-width: 208px) 100vw, 208px\" \/><\/figure><\/div>\n\n\n\n<div id=\"sol-mathcounts-exercises-12\" style=\"display:none\"><div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" src=\"https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2020\/10\/Screen-Shot-2020-01-14-at-10.09.19-AM.png\" alt=\"\" class=\"wp-image-227\" width=\"208\" height=\"256\" srcset=\"https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2020\/10\/Screen-Shot-2020-01-14-at-10.09.19-AM.png 416w, https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2020\/10\/Screen-Shot-2020-01-14-at-10.09.19-AM-244x300.png 244w\" sizes=\"(max-width: 208px) 100vw, 208px\" \/><\/figure><\/div>\n<p><strong>Hint<\/strong> Draw the altitude from $A$ of $\\triangle{ABC}$ intersecting $\\overline{BC}$ at $F$ and $\\overline{DE}$ at $G$. Try to find the length of $\\overline{AF}$ and $\\overline{AG}$.<\/p><\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In $\\triangle{ABC}$, $\\overline{AB}=5$, $\\overline{AC}=6$, $\\overline{BC}=7$. Square $BCED$ is drawn along the side of $\\overline{BC}$, as shown in the following figure. Find the area of $\\triangle{ADE}$. Click here for the hint. Hint Draw the altitude from $A$ of $\\triangle{ABC}$ intersecting $\\overline{BC}$ &hellip; <a href=\"https:\/\/mathfun4kids.com\/mlog\/?p=225\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[9,11],"tags":[],"_links":{"self":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/225"}],"collection":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=225"}],"version-history":[{"count":4,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/225\/revisions"}],"predecessor-version":[{"id":231,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/225\/revisions\/231"}],"wp:attachment":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=225"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=225"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=225"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}