{"id":"act_quizme:math:q3:07","source_id":"act_quizme","source_item_id":"math-q3-07","external_id":"5e34c1878ed5b08b","program":"ACT","section":"math","category_code":null,"category":null,"subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":7,"scored":true,"layout_warning":null,"stem":"In rectangle ABCD shown, segments line segment B E B E ¯ and line segment CE C E ¯ partition the rectangle into 3 triangles. Given DE=7 D E = 7 centimeters, BE=26 B E = 26 centimeters, and CE=25 C E = 25 centimeters, what is the length, in centimeters, of line segment BC B C ¯ ? Rectangle ABCD with point E on line segment AD. See long description for more information Long Description of Figure 1 Figure 1 The image is a rectangle labeled, clockwise from the top left, A, B, C, D, and E. Line segment DE is labeled 7, line segment BE is labeled 26, and line segment CE is labeled 25. ×","stimulus":"","stimulus_html":null,"stem_html":"
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In rectangle ABCD shown, segments line segment B EBE¯ and line segment CECE¯ partition the rectangle into 3 triangles. Given DE=7DE=7 centimeters, BE=26BE=26 centimeters, and CE=25CE=25 centimeters, what is the length, in centimeters, of line segment BCBC¯?

\"Rectangle

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Figure 1
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The image is a rectangle labeled, clockwise from the top left, A, B, C, D, and E. Line segment DE is labeled 7, line segment BE is labeled 26, and line segment CE is labeled 25.
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","rationale_html":"

A. Incorrect. Use the Pythagorean theorem to calculate the missing side lengths in △ABE and △CDE. Start by using 72+DC2=252 to calculate DC=252-72=24 cm. Note that DC=AB because opposite sides of a rectangle are equal. Then, use AE2+242=262 to calculate AE=262-242=10 cm. You may have stopped here, but remember the problem asks you to solve for BC.

B. Incorrect. Use the Pythagorean theorem to calculate the missing side lengths in △ABE and △CDE. You may have used incorrect proportional reasoning and thought that since BE=CE+1, it had to be true that AE=DE+1=8. Then, you may have calculated 7+8=15.

C. Correct. Use the Pythagorean theorem to calculate the missing side lengths in △ABE and △CDE. Start by using 72+DC2=252 to calculate DC=252-72=24 cm. Note that DC=AB because opposite sides of a rectangle are equal. Then, use AE2+242=262 to calculate AE=262-242=10 cm. Note that AD=BC because opposite sides of a rectangle are equal. Since AD=AE+DE and AD=BC, it is also true that BC=AE+DE=10+7=17 cm.

D. Incorrect. Use the Pythagorean theorem to calculate the missing side lengths in △ABE and △CDE. Start by using 72+DC2=252 to calculate DC=252-72=24 cm. Note that DC=AB because opposite sides of a rectangle are equal. You may have stopped here, but remember the problem asks you to solve for BC.

","correct_answer":["C"],"equiv_key":"6ac3e2b15cba6bc610ef588a","has_media":true,"has_mathml":true,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"

10

","ord":0},{"label":"B","content_html":"

15

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17

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24

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