Difference between revisions of "2021 Fall AMC 10B Problems/Problem 13"
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label("$C$",(1.5,3.3333333),SW); | label("$C$",(1.5,3.3333333),SW); | ||
label("$D$",D,SE); | label("$D$",D,SE); | ||
− | label("$ | + | label("$E$",H,SE); |
− | label("$ | + | label("$F$",J,SE); |
− | label("$ | + | label("$G$",K,N); |
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</asy> | </asy> | ||
− | We see that | + | We see that <math>\bigtriangleup ADG \sim \bigtriangleup BEG \sim \bigtriangleup CFG</math> by AA similarity. |
==Solution 2== | ==Solution 2== |
Revision as of 16:52, 24 November 2021
Contents
[hide]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?
Solution 1
Let's split the triangle down the middle and label it:
We see that by AA similarity.
Solution 2
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.