Difference between revisions of "2021 Fall AMC 10B Problems/Problem 13"
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==Problem== | ==Problem== | ||
| − | + | A square with side length <math>3</math> is inscribed in an isosceles triangle with one side of the square along the base of the triangle. A square with side length <math>2</math> has two vertices on the other square and the other two on sides of the triangle, as shown. What is the area of the triangle? | |
| + | (The official problem came with a daigram...) | ||
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| + | <math>(\textbf{A})\: 19\frac14\qquad(\textbf{B}) \: 20\frac14\qquad(\textbf{C}) \: 21 \frac34\qquad(\textbf{D}) \: 22\frac12\qquad(\textbf{E}) \: 23\frac34</math> | ||
==Solution== | ==Solution== | ||
Revision as of 10:58, 23 November 2021
Problem
A square with side length 
is inscribed in an isosceles triangle with one side of the square along the base of the triangle. A square with side length 
has two vertices on the other square and the other two on sides of the triangle, as shown. What is the area of the triangle?
(The official problem came with a daigram...)
Solution
By similarity, the height is 
and the base is 
.
Thus the area is 
, or 
.
~Hefei417, or 陆畅 Sunny from China
See Also
| 2021 Fall AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
