{"status": "success", "data": {"description_md": "Isosceles triangles $T$ and $T'$ are not congruent but have the same area and the same perimeter. The sides of $T$ have lengths of $5,5,$ and $8$, while those of $T'$ have lengths of $a,a,$ and $b$. Which of the following numbers is closest to $b$?\n\n$\\textbf{(A)}\\ 3 \\qquad\\textbf{(B)}\\ 4 \\qquad\\textbf{(C)}\\ 5 \\qquad\\textbf{(D)}\\ 6 \\qquad\\textbf{(E)}\\ 8$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Isosceles triangles  <span class=\"katex--inline\">T</span>  and  <span class=\"katex--inline\">T'</span>  are not congruent but have the same area and the same perimeter. The sides of  <span class=\"katex--inline\">T</span>  have lengths of  <span class=\"katex--inline\">5,5,</span>  and  <span class=\"katex--inline\">8</span> , while those of  <span class=\"katex--inline\">T'</span>  have lengths of  <span class=\"katex--inline\">a,a,</span>  and  <span class=\"katex--inline\">b</span> . Which of the following numbers is closest to  <span class=\"katex--inline\">b</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 3 \\qquad\\textbf{(B)}\\ 4 \\qquad\\textbf{(C)}\\ 5 \\qquad\\textbf{(D)}\\ 6 \\qquad\\textbf{(E)}\\ 8</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2015 AMC 12A Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/15_amc12A_p21", "prev": "/problem/15_amc12A_p19"}}