Difference between revisions of "2013 AMC 10A Problems/Problem 3"

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We know that the area of <math>\triangle ABE</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=\boxed{\textbf{(E) }8}</math>
 
We know that the area of <math>\triangle ABE</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=\boxed{\textbf{(E) }8}</math>
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==Video Solution==
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https://www.youtube.com/watch?v=2vf843cvVzo?t=0
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~sugar_rush
  
 
==See Also==
 
==See Also==

Revision as of 22:18, 23 November 2020

Problem

Square $ABCD$ has side length $10$. Point $E$ is on $\overline{BC}$, and the area of $\triangle ABE$ is $40$. What is $BE$? [asy] pair A,B,C,D,E; A=(0,0); B=(0,50); C=(50,50); D=(50,0); E = (30,50);    draw(A--B);    draw(B--E);    draw(E--C); draw(C--D); draw(D--A); draw(A--E); dot(A); dot(B); dot(C); dot(D); dot(E); label("A",A,SW); label("B",B,NW); label("C",C,NE); label("D",D,SE); label("E",E,N);  [/asy]


$\textbf{(A)}\ 4\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 7\qquad\textbf{(E)}\ 8$

Solution

We know that the area of $\triangle ABE$ is equal to $\frac{AB(BE)}{2}$. Plugging in $AB=10$, we get $80 = 10BE$. Dividing, we find that $BE=\boxed{\textbf{(E) }8}$

Video Solution

https://www.youtube.com/watch?v=2vf843cvVzo?t=0

~sugar_rush

See Also

2013 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 4
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 AMC 10 Problems and Solutions
2013 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
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 AMC 12 Problems and Solutions

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