2019 AMC 8 Problems/Problem 4
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
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 |
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