Try this beautiful problem from Geometry: Side of Square.
Sides of Square – AMC-10A, 2013- Problem 3
Square $ABCD$ has side length $10$. Point $E$ is on $\overline{BC}$, and the area of $\triangle ABE$ is $40$. What is $BE$?
,
i
- $4$
- $5$
- $6$
- $7$
- \(8\)
Key Concepts
Geometry
Square
Triangle
Check the Answer
Answer: $8$
AMC-10A (2013) Problem 3
Pre College Mathematics
Try with Hints
Given that Square $ABCD$ has side length $10$ and area of $\triangle ABE$ is $40$.we have to find out length of \(BE\) where \(E\) is the point on \(BC\). we know area of the \(\triangle ABE=\frac{1}{2} AB.BE=40\)
Can you find out the side length of \(BE\)?
Can you now finish the problem ……….
\(\triangle ABE=\frac{1}{2} AB.BE=40\)
\(\Rightarrow \triangle ABE=\frac{1}{2} 10.BE=40\)
\(\Rightarrow \triangle ABE=\frac{1}{2} 10.BE=40\)
\(\Rightarrow BE=8\)
Other useful links
- https://www.cheenta.com/surface-area-of-cube-amc-10a-2007-problem-21/
- https://www.youtube.com/watch?v=VLyrlx2DWdA&t=20s