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AMC 10 Geometry Math Olympiad USA Math Olympiad

Side of Square | AMC 10A, 2013 | Problem 3

Try this beautiful problem from Geometry: Side of Square from AMC-10A (2013) Problem 3. You may use sequential hints to solve the problem.

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 $BE$?

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Side of Square - Problem
  • $4$
  • $5$
  • $6$
  • $7$
  • \(8\)

Key Concepts


Geometry

Square

Triangle

Check the Answer


But try the problem first…

Answer: $8$

Source
Suggested Reading

AMC-10A (2013) Problem 3

Pre College Mathematics

Try with Hints


First hint

Side of Square

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 ……….

Second Hint

Side of Square

\(\triangle ABE=\frac{1}{2} AB.BE=40\)

\(\Rightarrow \triangle ABE=\frac{1}{2} 10.BE=40\)

\(\Rightarrow \triangle ABE=\frac{1}{2} 10.BE=40\)

\(\Rightarrow BE=8\)

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