Difference between revisions of "2019 AMC 8 Problems"
Phoenixfire (talk | contribs) (→Problem 4) |
Phoenixfire (talk | contribs) (→Problem 4) |
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label("C",(13,0),E); | label("C",(13,0),E); | ||
label("D",(0,-5),S); | label("D",(0,-5),S); | ||
| + | </asy> | ||
| + | |||
| + | == Solution == | ||
| + | Because it is a rhombus all sides are equal. Implies all sides are 13. In a rhombus diagonals are perpendicular. | ||
| + | |||
| + | <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); | ||
| + | draw((-13,0)--(13,0)) | ||
| + | draw((0,5,)--(0,-5)) | ||
</asy> | </asy> | ||
Revision as of 00:51, 20 November 2019
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Solution
- 6 Problem 5
- 7 Problem 6
- 8 Problem 7
- 9 Problem 8
- 10 Problem 9
- 11 Problem 10
- 12 Problem 11
- 13 Problem 12
- 14 Problem 13
- 15 Problem 14
- 16 Problem 15
- 17 Problem 16
- 18 Problem 17
- 19 Problem 18
- 20 Problem 19
- 21 Problem 20
- 22 Problem 21
- 23 Problem 22
- 24 Problem 23
- 25 Problem 24
- 26 Problem 25
Problem 1
Ike and Mike go into a sandwich shop with a total of 
to spend. Sandwiches cost 
each and soft drinks cost 
each. Ike and Mike plan to buy as many sandwiches as they can and use the remaining money to buy soft drinks. Counting both soft drinks and sandwiches, how many items will they buy?
Problem 2
![[asy] draw((0,0)--(3,0)); draw((0,0)--(0,2)); draw((0,2)--(3,2)); draw((3,2)--(3,0)); dot((0,0)); dot((0,2)); dot((3,0)); dot((3,2)); draw((2,0)--(2,2)); draw((0,1)--(2,1)); label("A",(0,0),S); label("B",(3,0),S); label("C",(3,2),N); label("D",(0,2),N); [/asy]](http://latex.artofproblemsolving.com/e/0/7/e0752885e3cff488bd89893347c595b7c570d339.png)
Three identical rectangles are put together to form rectangle , as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is 
feet, what is the area in square feet of rectangle 
?
(A) 45 (B) 75 (C) 100 (D) 125 (E) 150
Problem 3
3. Which of the following is the correct order of the fractions 
, 
, and 
, from least to greatest?
Problem 4
Quadrilateral is a rhombus with perimeter 
meters. The length of diagonal 
is 
meters. What is the area in square meters of rhombus ?
![[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]](http://latex.artofproblemsolving.com/e/5/4/e54b35c6e9f6a1eaa16a3138ed06ebc73122be63.png)
Solution
Because it is a rhombus all sides are equal. Implies all sides are 13. In a rhombus diagonals are perpendicular.
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);
draw((-13,0)--(13,0))
draw((0,5,)--(0,-5))
(Error making remote request. Unknown error_msg)
