Difference between revisions of "2019 AMC 8 Problems/Problem 4"
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− | == Solution == | + | == Problem 4 == |
+ | |||
+ | Quadrilateral <math>ABCD</math> is a rhombus with perimeter <math>52</math> meters. The length of diagonal <math>\overline{AC}</math> is <math>24</math> meters. What is the area in square meters of rhombus <math>ABCD</math>? | ||
+ | |||
+ | <asy> | ||
+ | draw((-13,0)--(0,5)); | ||
+ | draw((0,5)--(13,0)); | ||
+ | draw((13,0)--(0,-5)); | ||
+ | draw((0,-5)--(-13,0)); | ||
+ | dot((-13,0)); | ||
+ | dot((0,5)); | ||
+ | dot((13,0)); | ||
+ | dot((0,-5)); | ||
+ | label("A",(-13,0),W); | ||
+ | label("B",(0,5),N); | ||
+ | label("C",(13,0),E); | ||
+ | label("D",(0,-5),S); | ||
+ | </asy> | ||
+ | |||
+ | <math>\textbf{(A) }60\qquad\textbf{(B) }90\qquad\textbf{(C) }105\qquad\textbf{(D) }120\qquad\textbf{(E) }144</math> | ||
+ | |||
+ | |||
+ | == Solution 1 == | ||
<asy> | <asy> | ||
draw((-12,0)--(0,5)); | draw((-12,0)--(0,5)); |
Revision as of 13:09, 20 November 2019
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
Because it is a rhombus all sides are equal. Implies all sides are 13. In a rhombus diagonals are perpendicular and bisect each other. Which means = = .
Consider one of the right triangles.
= . = . Which means = .
Thus the values of the two diagonals are = and = . Which means area = = =
~phoenixfire
See Also
2019 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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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