AMC 10 USA Math Olympiad

Finding side of a triangle | AMC 10A, 2013 | problem 3

Try this beautiful problem from AMC 10. It involves geometry of triangles. We provide sequential hints so that you can try the problem.

Finding Side of Triangle

The area of a triangle is defined as the total space that is enclosed by any particular triangle. The basic formula to find the area of a given triangle is A = 1/2 × b × h, where b is the base and h is the height of the given triangle, whether it is scalene, isosceles or equilateral. This problem is based on finding side of a triangle by its area.

Try the Problem

This problem is from AMC 10A, 2013.

Square $ABCD$ has a side length $10$. The point $E$ is on $\overline{BC}$ and the area of $\triangle ABE$ is $40$. What is $\overline{BE}?$

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

Finding side BE

AMC 10A, 2013 Problem 3

Area of Triangle


Challenges and Thrills in Pre College Mathematics

Excursion of Mathematics

Knowledge Graph

Area of triangle- Knowledge Graph

Use some hints

Given, Square  ABCD  has side length 10.

So, AB = 10.

Now, we know area of a triangle =$\frac{(\text{height})\times(\text{base})}{2}$. Try to use this here

So we have the area of $\triangle ABE$ is equal to $\frac{AB\times BE}{2}$. Plugging in $AB=10$. What we get?

We get $10\times BE=80 \Rightarrow BE=8$

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