Difference between revisions of "2013 AMC 10A Problems/Problem 3"
(Created page with "Square <math> ABCD </math> has side length <math>10</math>. Point <math>E</math> is on <math>\overline{BC}</math>, and the area of <math> \triangle ABE </math> is <math>40</math>...") |
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<math> \textbf{(A)}\ 4\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 7\qquad\textbf{(E)}\ 8 </math> | <math> \textbf{(A)}\ 4\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 7\qquad\textbf{(E)}\ 8 </math> | ||
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+ | We know that the area of <math>\triangle ABC</math> is equal to <math>\frac{AB(BE)}{2}</math>. Plugging in <math>AB=10</math>, we get <math>80 = 10BE</math>. Dividing, we find that <math>BE=8</math>, <math>\textbf{(E)}</math> |
Revision as of 17:49, 7 February 2013
Square has side length
. Point
is on
, and the area of
is
. What is
?
[asy]
size(150);
pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps);
draw((0,0)--(0,10)--(10,10)--(10,0)--(0,0)--(6,10));
dot((0,0));
dot((0,10));
dot((10,10));
dot((10,0));
dot((6,10));
label("",(0,0),SW);
label("
",(0,10),NW);
label("
",(10,10),NE);
label("
",(10,0),SE);
label("
",(6,10),N);[/asy]
We know that the area of is equal to
. Plugging in
, we get
. Dividing, we find that
,