Difference between revisions of "2023 AMC 12B Problems/Problem 11"
m (changed shorten to shorter (grammar)) |
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==Solution== | ==Solution== | ||
− | Denote by <math>x</math> the length of the | + | Denote by <math>x</math> the length of the shorter base. |
Thus, the height of the trapezoid is | Thus, the height of the trapezoid is | ||
<cmath> | <cmath> |
Revision as of 19:45, 15 November 2023
Solution
Denote by the length of the shorter base.
Thus, the height of the trapezoid is
Thus, the area of the trapezoid is
where the inequality follows from the AM-GM inequality and it is binding if and only if .
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)