## 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 $

AMC 10A, 2013 Problem 3

Area of Triangle

4/10

Challenges and Thrills in Pre College Mathematics

Excursion of Mathematics

## Knowledge Graph

## Use some hints

First Hint

Given, Square ** ABCD** has side length** 10**.

So,** AB = 10.**

Second Hint

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

Third Hint

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

Final Step

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

## Other useful links

- https://www.cheenta.com/combinatorics-amc-8-2008-problem-14/
- https://www.youtube.com/watch?v=L4awwIFiBq4