Difference between revisions of "1987 AHSME Problems/Problem 2"
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==Solution== | ==Solution== | ||
− | <math>\triangle</math> DBE is similar to <math>\triangle</math> ABC by AA, so <math>\overline{DE}</math> = 1 by similarity, and <math>\overline{CE} = \overline{AD} = 2</math>, by subtraction. Thus the perimeter is <math>3+2+2+1 = 8</math>, or <math>\boxed{E}</math> | + | <math>\triangle</math> DBE is similar to <math>\triangle</math> ABC by AA, so <math>\overline{DE}</math> = 1 by similarity, and <math>\overline{CE} = \overline{AD} = 2</math>, by subtraction. Thus the perimeter is <math>3+2+2+1 = 8</math>, or <math>\boxed{E}</math>. -slackroadia |
== See also == | == See also == |
Revision as of 17:37, 23 April 2017
Problem
A triangular corner with side lengths is cut from equilateral triangle ABC of side length . The perimeter of the remaining quadrilateral is
Solution
DBE is similar to ABC by AA, so = 1 by similarity, and , by subtraction. Thus the perimeter is , or . -slackroadia
See also
1987 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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All AHSME Problems and Solutions |
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