{"status": "success", "data": {"description_md": "Daniel finds a rectangular index card and measures its diagonal to be $8$ centimeters.\nDaniel then cuts out equal squares of side $1$ cm at two opposite corners of the index card and measures the distance between the two closest vertices of these squares to be $4\\sqrt{2}$ centimeters, as shown below. What is the area of the original index card?\n\n<center>\n<img class=\"problem-image\" height=\"175\" src=\"https://latex.artofproblemsolving.com/2/2/f/22f9f7a96f6ad58ba5a6b8396b925cd53152cf24.png\" width=\"335\"/>\n</center><br>\n\n$\\textbf{(A) } 14 \\qquad \\textbf{(B) } 10\\sqrt{2} \\qquad \\textbf{(C) } 16 \\qquad \\textbf{(D) } 12\\sqrt{2} \\qquad \\textbf{(E) } 18$", "description_html": "<p>Daniel finds a rectangular index card and measures its diagonal to be <span class=\"katex--inline\">8</span> centimeters.<br/>&#10;Daniel then cuts out equal squares of side <span class=\"katex--inline\">1</span> cm at two opposite corners of the index card and measures the distance between the two closest vertices of these squares to be <span class=\"katex--inline\">4\\sqrt{2}</span> centimeters, as shown below. What is the area of the original index card?</p>&#10;<center>&#10;<img class=\"problem-image\" height=\"175\" src=\"https://latex.artofproblemsolving.com/2/2/f/22f9f7a96f6ad58ba5a6b8396b925cd53152cf24.png\" width=\"335\"/>&#10;</center><br/>&#10;<p><span class=\"katex--inline\">\\textbf{(A) } 14 \\qquad \\textbf{(B) } 10\\sqrt{2} \\qquad \\textbf{(C) } 16 \\qquad \\textbf{(D) } 12\\sqrt{2} \\qquad \\textbf{(E) } 18</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 1, "problem_name": "2022 AMC 10A Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc10A_p11", "prev": "/problem/22_amc10A_p09"}}