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AMC 10 USA Math Olympiad

2D Geometry AMC 8, 2019 Problem 2

Try this beautiful problem from AMC 10. It involves geometry of triangles. We provide sequential hints so that you can try the problem.

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What are we learning ?

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Competency in Focus: 2D Geometry (Area of Rectangle)

This problem from American Mathematics contest (AMC 8, 2019) is based on calculation of area of  Rectangle .

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First look at the knowledge graph

[/et_pb_text][et_pb_image src=”https://www.cheenta.com/wp-content/uploads/2020/02/drawit-diagram-4.png” align=”center” force_fullwidth=”on” _builder_version=”4.2.2″ min_height=”378px” height=”187px” max_height=”207px” hover_enabled=”0″ box_shadow_style=”preset6″ box_shadow_color=”#0c71c3″ alt=”knowledge graph of area of rectangle” title_text=”knowledge graph of Area of rectangle”][/et_pb_image][et_pb_text _builder_version=”3.27.4″ text_font=”Raleway|300|||||||” text_text_color=”#ffffff” header_font=”Raleway|300|||||||” header_text_color=”#e2e2e2″ background_color=”#0c71c3″ custom_padding=”20px|20px|20px|20px” border_radii=”on|5px|5px|5px|5px” box_shadow_style=”preset3″ inline_fonts=”Aclonica”]

Next understand the problem

[/et_pb_text][et_pb_text _builder_version=”4.2.2″ text_font=”Raleway||||||||” text_font_size=”20px” text_letter_spacing=”1px” text_line_height=”1.5em” background_color=”#f4f4f4″ custom_margin=”10px||10px” custom_padding=”10px|20px|10px|20px” box_shadow_style=”preset2″]Three identical rectangles are put together to form rectangle $ABCD$, as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is 5 feet, what is the area in square feet of rectangle $ABCD$?  [/et_pb_text][/et_pb_column][/et_pb_row][et_pb_row _builder_version=”4.0″][et_pb_column type=”4_4″ _builder_version=”3.25″ custom_padding=”|||” custom_padding__hover=”|||”][et_pb_accordion open_toggle_text_color=”#0c71c3″ _builder_version=”4.2.2″ toggle_font=”||||||||” body_font=”Raleway||||||||” text_orientation=”center” custom_margin=”10px||10px” hover_enabled=”0″][et_pb_accordion_item title=”Source of the problem” _builder_version=”4.2.2″ open=”off”]American Mathematical Contest 2019, AMC 8  Problem 2[/et_pb_accordion_item][et_pb_accordion_item title=”Key Competency” open=”on” _builder_version=”4.2.2″]

2D Geometry (Area of Rectangle)

[/et_pb_accordion_item][et_pb_accordion_item title=”Difficulty Level” _builder_version=”4.2.2″ open=”off”]3/10[/et_pb_accordion_item][et_pb_accordion_item title=”Suggested Book” _builder_version=”4.2.2″ open=”off”]Challenges and Thrills in Pre College Mathematics  [/et_pb_accordion_item][/et_pb_accordion][et_pb_text _builder_version=”4.0.9″ text_font=”Raleway|300|||||||” text_text_color=”#ffffff” header_font=”Raleway|300|||||||” header_text_color=”#e2e2e2″ background_color=”#0c71c3″ custom_margin=”48px||48px” custom_padding=”20px|20px|0px|20px||” border_radii=”on|5px|5px|5px|5px” box_shadow_style=”preset3″ inline_fonts=”Aclonica”]

Start with hints 

[/et_pb_text][et_pb_tabs _builder_version=”4.2.2″][et_pb_tab title=”HINT 0″ _builder_version=”4.0.9″]Do you really need a hint? Try it first![/et_pb_tab][et_pb_tab title=”HINT 1″ _builder_version=”4.2.2″]The length of the smaller side of each rectangle is given 5 feet. So using the diagram we can find  that the larger side of the small rectangle is 2 times the length of the smaller side.[/et_pb_tab][et_pb_tab title=”HINT 2″ _builder_version=”4.2.2″]So find the longer side which is 5*2 = 10 feet.[/et_pb_tab][et_pb_tab title=”HINT 3″ _builder_version=”4.2.2″] the area of the identical rectangles is 5*10 = 50 square feet[/et_pb_tab][et_pb_tab title=”HINT 4″ _builder_version=”4.2.2″]  Thus at end we have 3 identical rectangles formed a bigger rectangle……Try to solve …   50*3 = 150 square feet [/et_pb_tab][/et_pb_tabs][/et_pb_column][/et_pb_row][/et_pb_section][et_pb_section fb_built=”1″ fullwidth=”on” _builder_version=”4.2.2″ global_module=”50833″][et_pb_fullwidth_header title=”AMC – AIME Program” button_one_text=”Learn More” button_one_url=”https://www.cheenta.com/amc-aime-usamo-math-olympiad-program/” header_image_url=”https://www.cheenta.com/wp-content/uploads/2018/03/matholympiad.png” _builder_version=”4.2.2″ title_level=”h2″ background_color=”#00457a” custom_button_one=”on” button_one_text_color=”#44580e” button_one_bg_color=”#ffffff” button_one_border_color=”#ffffff” button_one_border_radius=”5px”]

AMC – AIME – USAMO Boot Camp for brilliant students. Use our exclusive one-on-one plus group class system to prepare for Math Olympiad

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