// Numbas version: exam_results_page_options
{"name": "Simon's copy of Q3 Triangle problems", "extensions": [], "custom_part_types": [], "resources": [["question-resources/area-of-a-equilateral-triangle-formula.png", "/srv/numbas/media/question-resources/area-of-a-equilateral-triangle-formula.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "<p><strong>(a)</strong></p>\n<p>Use the formula for area&nbsp;of a triangle in terms of perpendicular height, $h$ and base, $b$</p>\n<p>Area&nbsp;= $\\frac{1}{2}&nbsp;\\times b&nbsp; \\times h$</p>\n<p>In this case</p>\n<p>$\\var{area2} = \\frac{1}{2}&nbsp;\\times \\var{lent2}&nbsp; \\times h$</p>\n<p>So $h = 2 \\times \\frac{\\var{area2}}{\\var{lent2}} = \\var{precround(ans2,2)}$m</p>\n<p><strong>&nbsp;</strong></p>\n<p><strong>(b)</strong></p>\n<p>Using the given formula&nbsp;$A =\\frac{\\sqrt{3}}{4}&nbsp;a^2&nbsp;= \\frac{\\sqrt3}{4} \\times \\var{side1}^2= \\var{precround(ans1,2)}$m$^2$</p>\n<p><strong></strong></p>\n<p><strong></strong></p>\n<p>An alternative method uses the area of triangle formula&nbsp;$A = \\frac{1}{2}$ab $\\sin(c)$ =&nbsp;$\\frac{1}{2}&nbsp;\\times \\var{side1} \\times \\var{side1} \\times&nbsp;\\sin(60) = \\var{precround(ans1,2)}$m$^2$</p>\n<p></p>\n<p></p>", "variables": {"ans1": {"name": "ans1", "definition": "(sqrt(3)/4)*side1^2", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "lent2": {"name": "lent2", "definition": "random(7..12#0.5)", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "ans2": {"name": "ans2", "definition": "(2*area2)/lent2", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "area2": {"name": "area2", "definition": "random(60..70#0.1)", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "side1": {"name": "side1", "definition": "random(12..16#0.25)", "description": "", "group": "Ungrouped variables", "templateType": "anything"}}, "variable_groups": [], "ungrouped_variables": ["side1", "ans1", "lent2", "area2", "ans2"], "preamble": {"css": "", "js": ""}, "tags": [], "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "name": "Simon's copy of Q3 Triangle problems", "statement": "<p>Give answers correct to <strong>2 decimal places</strong></p>", "metadata": {"description": "<p>Areas of triangles</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "functions": {"tri": {"parameters": [["h", "number"]], "language": "javascript", "type": "html", "definition": "        var c = document.createElement('canvas');\n        $(c).attr('width',200).attr('height',200);\n        var context = c.getContext('2d');\n        \nvar height = 100 * (Math.sqrt(3)/2);\nvar XX = 100\nvar YY = 100\n\n// the triangle\ncontext.beginPath();\ncontext.moveTo(100, 100);\ncontext.lineTo(XX+50, YY+height);\ncontext.lineTo(XX-50, YY+height);\ncontext.closePath();\n \n// the outline\ncontext.lineWidth = 10;\ncontext.strokeStyle = '#666666';\ncontext.stroke();\n \n// the fill color\ncontext.fillStyle = \"#FFCC00\";\ncontext.fill();\n\n        return c;\n      "}, "tri1": {"parameters": [["a", "number"]], "language": "javascript", "type": "html", "definition": "        var c = document.createElement('canvas');\n        $(c).attr('width',500).attr('height',500);\n        var context = c.getContext('2d');\n        \nvar height = 100 * (Math.sqrt(3)/2);\nvar XX = 200\nvar YY = 200\n\n// the triangle\ncontext.beginPath();\ncontext.moveTo(100, 100);\ncontext.lineTo(XX+50, YY+height);\ncontext.lineTo(XX-50, YY+height);\ncontext.closePath();\n \n// the outline\ncontext.lineWidth = 10;\ncontext.strokeStyle = '#666666';\ncontext.stroke();\n \n// the fill color\ncontext.fillStyle = \"#FFCC00\";\ncontext.fill();\n\n        return c;\n      "}}, "extensions": [], "parts": [{"showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "gapfill", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "sortAnswers": false, "prompt": "<p>Calculate the perpendicular height of a&nbsp;triangle whose&nbsp;base length is&nbsp;$\\var{lent2}$m, if the area of this triangle is&nbsp;$\\var{area2}$m$^2$</p>\n<p>[[0]]m</p>\n<p></p>", "marks": 0, "gaps": [{"mustBeReduced": false, "unitTests": [], "minValue": "{ans2}", "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"], "maxValue": "{ans2}", "marks": 1, "showPrecisionHint": false, "allowFractions": false, "showCorrectAnswer": true, "strictPrecision": false, "variableReplacementStrategy": "originalfirst", "precisionMessage": "You have not given your answer to the correct precision.", "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "variableReplacements": [], "correctAnswerFraction": false, "scripts": {}, "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "precision": "2", "precisionType": "dp", "precisionPartialCredit": 0}]}, {"showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "gapfill", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "sortAnswers": false, "prompt": "<p>The area of an equilateral triangle with side length $a$ is given by $A =\\frac{\\sqrt{3}}{4}&nbsp;a^2$</p>\n<p>Hence find the area of an equilateral triangle which has a side of $\\var{side1}$m.</p>\n<p>{tri(side1)}</p>\n<p>[[0]]m$^2$</p>", "marks": 0, "gaps": [{"mustBeReduced": false, "unitTests": [], "minValue": "{ans1}", "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"], "maxValue": "{ans1}", "marks": 1, "showPrecisionHint": false, "allowFractions": false, "showCorrectAnswer": true, "strictPrecision": false, "variableReplacementStrategy": "originalfirst", "precisionMessage": "You have not given your answer to the correct precision.", "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "variableReplacements": [], "correctAnswerFraction": false, "scripts": {}, "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "precision": "2", "precisionType": "dp", "precisionPartialCredit": 0}]}], "type": "question", "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}