Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2003 AMC 8 Problems/Problem 6"

(Created page with "==Problem 6== Given the areas of the three squares in the figure, what is the area of the interior triangle? File:AMC8 problem 6 2003image.png <math>\mathrm{(A)}\ 13 \qquad...")
 
m (→‎Problem 6)
Line 1: Line 1:
−
==Problem 6==
+
==Problem==
 
Given the areas of the three squares in the figure, what is the area of the interior triangle?  [[File:AMC8 problem 6 2003image.png]]
 
Given the areas of the three squares in the figure, what is the area of the interior triangle?  [[File:AMC8 problem 6 2003image.png]]
  

Revision as of 15:23, 29 July 2011

Problem

Given the areas of the three squares in the figure, what is the area of the interior triangle? AMC8 problem 6 2003image.png

$\mathrm{(A)}\ 13 \qquad\mathrm{(B)}\ 30 \qquad\mathrm{(C)}\ 60 \qquad\mathrm{(D)}\ 300 \qquad\mathrm{(E)}\ 1800$

Solution

The sides of the squares are $5, 12$ and $13$ for the square with area $25, 144$ and $169$, respectively. The legs of the interior triangle are $5$ and $12$, so the area is $\frac{5 \times 12}{2}=\boxed{\mathrm{(B)}\ 30}$

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2003_AMC_8_Problems/Problem_6&oldid=40901"