{"id":"cb_question_bank:373bd807-a1c1-4485-93f9-0e12cce12145","source_id":"cb_question_bank","source_item_id":"373bd807-a1c1-4485-93f9-0e12cce12145","external_id":"2ed3a51e-14c9-41a5-8246-b0df7d098ee8","ibn":null,"question_id":"997bec28","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.A.","skill":"Linear equations in one variable","difficulty":"E","score_band":2,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The perimeter of an isosceles triangle is 83 inches. Each of the two congruent sides of the triangle has a length of 24 inches. What is the length, in inches, of the third side?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The perimeter of an isosceles triangle is <math alttext=\"83\"><mn>83</mn>\n</math> inches. Each of the two congruent sides of the triangle has a length of <math alttext=\"24\"><mn>24</mn>\n</math> inches. What is the length, in inches, of the third side?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"35\"><mn>35</mn>\n</math>. It’s given that the perimeter of an isosceles triangle is <math alttext=\"83\"><mn>83</mn></math> inches and that each of the two congruent sides has a length of <math alttext=\"24\"><mn>24</mn></math> inches. The perimeter of a triangle is the sum of the lengths of its three sides. The equation <math alttext=\"24 plus 24 plus x equals 83\"><mn>24</mn><mo>+</mo><mn>24</mn><mo>+</mo><mi>x</mi><mo>=</mo><mn>83</mn></math> can be used to represent this situation, where <math alttext=\"x\"><mi>x</mi>\n</math> is the length, in inches, of the third side. Combining like terms on the left-hand side of this equation yields <math alttext=\"48 plus x equals 83\"><mn>48</mn><mo>+</mo><mi>x</mi><mo>=</mo><mn>83</mn></math>. Subtracting <math alttext=\"48\"><mn>48</mn>\n</math> from both sides of this equation yields <math alttext=\"x equals 35\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>35</mn>\n</mrow>\n</math>. Therefore, the length, in inches, of the third side is <math alttext=\"35\"><mn>35</mn></math>.</p>","correct_answer":["35"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.808000+00:00","source_updated_at":"2023-08-02T20:25:59.808000+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}}