Difference between revisions of "2019 AMC 8 Problems/Problem 4"
(→See Also) |
(→Solution 1) |
||
Line 66: | Line 66: | ||
Video Solution (Also includes problems 1-10)= https://www.youtube.com/watch?v=5i69xiEF-pk&t=2s | Video Solution (Also includes problems 1-10)= https://www.youtube.com/watch?v=5i69xiEF-pk&t=2s | ||
+ | |||
+ | == Solution 2 == | ||
+ | <asy> | ||
+ | draw((-12,0)--(0,5)); | ||
+ | draw((0,5)--(12,0)); | ||
+ | draw((12,0)--(0,-5)); | ||
+ | draw((0,-5)--(-12,0)); | ||
+ | draw((0,0)--(12,0)); | ||
+ | draw((0,0)--(0,5)); | ||
+ | draw((0,0)--(-12,0)); | ||
+ | draw((0,0)--(0,-5)); | ||
+ | dot((-12,0)); | ||
+ | dot((0,5)); | ||
+ | dot((12,0)); | ||
+ | dot((0,-5)); | ||
+ | label("A",(-12,0),W); | ||
+ | label("B",(0,5),N); | ||
+ | label("C",(12,0),E); | ||
+ | label("D",(0,-5),S); | ||
+ | label("E",(0,0),SW); | ||
+ | </asy> | ||
==See also== | ==See also== |
Revision as of 12:19, 2 November 2020
Contents
Problem 4
Quadrilateral is a rhombus with perimeter meters. The length of diagonal is meters. What is the area in square meters of rhombus ?
Solution 1
A rhombus has sides of equal length. Because the perimeter of the rhombus is , each side is . In a rhombus, diagonals are perpendicular and bisect each other, which means = = .
Consider one of the right triangles:
= , and = . Using Pythagorean theorem, we find that = . "You may recall the famous pythagorean triple, (5, 12, 13), that's how I did it"-Zack2008
Thus the values of the two diagonals are = and = . The area of a rhombus is = = =
~phoenixfire
Video Solution (Also includes problems 1-10)= https://www.youtube.com/watch?v=5i69xiEF-pk&t=2s
Solution 2
See also
2019 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.