2005 AMC 8 Problems/Problem 9
Contents
Problem
In quadrilateral , sides and both have length 10, sides and both have length 17, and the measure of angle is . What is the length of diagonal ?
Solutions
Solution 1
Because , is an isosceles triangle with . Angles in a triangle add up to , and since , the other two angles are also , and is an equilateral triangle. Therefore .
Solution 2
We can divide in half and connect this point to A, dividing in half. This means the base will be and the hypotenuse will be 17. By using the Pythagorean's Theorem, we see that if the base and height are shared, the hypotenuse should be the same. This tells us that the length of .
~Champion1234
Solution 3 (Easiest)
Take an equilateral triangle with side length . is congruent to this by , hence it is equilateral. The answer is .
~yofro
Video Solution by OmegaLearn
https://youtu.be/abSgjn4Qs34?t=3034
~pi_is_3.14
See Also
2005 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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 AJHSME/AMC 8 Problems and Solutions |
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