Difference between revisions of "2009 AMC 8 Problems/Problem 7"
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− | The triangular plot of ACD lies between Aspen Road, Brown Road and a railroad. Main Street runs east and west, and the railroad runs north and south. The numbers in the diagram indicate distances in miles. The width of the railroad track can be ignored. | + | ==Problem== |
+ | |||
+ | The triangular plot of ACD lies between Aspen Road, Brown Road and a railroad. Main Street runs east and west, and the railroad runs north and south. The numbers in the diagram indicate distances in miles. The width of the railroad track can be ignored. How many square miles are in the plot of land ACD? | ||
+ | |||
<asy> | <asy> | ||
size(250); | size(250); | ||
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label(rotate(63.43494882)*"Brown", A--D, NW); | label(rotate(63.43494882)*"Brown", A--D, NW); | ||
</asy> | </asy> | ||
− | <math>\textbf{(A)}\ 2\qquad | + | |
− | \textbf{(B)}\ 3 \qquad | + | <math>\textbf{(A)}\ 2\qquad \textbf{(B)}\ 3 \qquad \textbf{(C)}\ 4.5 \qquad \textbf{(D)}\ 6 \qquad \textbf{(E)}\ 9</math> |
− | \textbf{(C)}\ 4.5 \qquad | + | |
− | \textbf{(D)}\ 6 \qquad | + | ==Solution== |
− | \textbf{(E)}\ 9</math> | + | The area of a triangle is <math>\frac12 bh</math>. If we let <math>CD</math> be the base of the triangle, then the height is <math>AB</math>, and the area is <math>\frac12 \cdot 3 \cdot 3 = \boxed{\textbf{(C)}\ 4.5}</math>. |
+ | |||
+ | ==Video Solution== | ||
+ | https://www.youtube.com/watch?v=Opz71P5o4uI | ||
+ | |||
+ | ==See Also== | ||
+ | {{AMC8 box|year=2009|num-b=6|num-a=8}} | ||
+ | {{MAA Notice}} |
Latest revision as of 18:22, 10 June 2022
Contents
Problem
The triangular plot of ACD lies between Aspen Road, Brown Road and a railroad. Main Street runs east and west, and the railroad runs north and south. The numbers in the diagram indicate distances in miles. The width of the railroad track can be ignored. How many square miles are in the plot of land ACD?
Solution
The area of a triangle is . If we let be the base of the triangle, then the height is , and the area is .
Video Solution
https://www.youtube.com/watch?v=Opz71P5o4uI
See Also
2009 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
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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