{"id":"cb_question_bank:8aa3cb25-a471-4d9f-8a8b-a7015a5e3c20","source_id":"cb_question_bank","source_item_id":"8aa3cb25-a471-4d9f-8a8b-a7015a5e3c20","external_id":null,"ibn":"06375-DC","question_id":"58dcc59f","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"H","score_band":6,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104&nbsp;square feet, what will be the length, in feet, of the garden?</p>\n","rationale_html":"<p>The correct answer is 13. Let <span class=\"italic\">w</span> represent the width of the rectangular garden, in feet. Since the length of the garden will be 5 feet longer than the width of the garden, the length of the garden will be <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/780a778f31ae0b1eac599f230cd2d1b2d8ac11e11598490f4ae11d05453c66a8\" alt=\"w plus 5\"></span> feet. Thus the area of the garden will be <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/65086a955ccd11e62487b1a5f365606c2215b34a701d42a8c63b260b783044c7\" alt=\"w times, open parenthesis, w plus 5, close parenthesis\"></span>. It is also given that the area of the garden will be 104 square feet. Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4dff0d5cf7ba01e5db15ee86585175840d30e5dc7110ebf8aeed4e80f5a2db46\" alt=\"w times, open parenthesis, w plus 5, close parenthesis, equals 104\"></span>, which is equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b338efe8e0dff766bb279c1104d828b77b6a108bc796b9c5a0f27682f9d8e16f\" alt=\"w squared, plus 5 w, minus 104, equals 0\"></span>. Factoring this equation results in <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f3017c3d3cb35e5eab1238ebd1a54126b393f629bcd1f78c4398994bb795f49b\" alt=\"open parenthesis, w plus 13, close parenthesis, times, open parenthesis, w minus 8, close parenthesis, equals 0\"></span>. Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cc58229aaf96075754637a5b4ae0f3f696ea215c00025e25d6f37772a582dbe7\" alt=\"w equals 8\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dbcb1ee0f6a654224951dd631ebcc2089b040ef111cb856806f54a4734f61f18\" alt=\"w equals negative 13\"></span>. Because width cannot be negative, the width of the garden must be 8 feet. This means the length of the garden must be <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/22f68ec118d242241f57498fa2330567652cd17e9d9297feec36634344da4c60\" alt=\"8 plus 5, equals 13\"></span> feet.</p>\n","correct_answer":["13"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.630000+00:00","source_updated_at":"2023-08-02T20:25:59.630000+00:00","options":[],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}