Geometry Puzzle – Challenge 76
This is a perfect math challenge for those who enjoy solving complicated mathematics and critical thinking challenges. Let's challenge your brain!

Challenge:
If the perimeter of an equilateral triangle is 2x meters and its area is x square meters, then what is the length of one side of the triangle in meters?
A- \(\sqrt{3}\)
B- \(\frac{\sqrt{3}}{2}\)
C- \(2\sqrt{3}\)
D- \(\frac{2\sqrt{3}}{3}\)
E- 3
The Absolute Best Book to challenge your Smart Student!

The correct answer is C.
The perimeter of the equilateral triangle is 2x meters. So, one side is \(\frac{2}{3}x \) meters.
The area of an equilateral triangle \(= \frac{s^2 \sqrt{3}}{4}\) (s is one side of the triangle)
The perimeter of the triangle is twice its area. So:
\(2x = 2 (\frac{s^2 \sqrt{3}}{4}) → 2x = (\frac{s^2 \sqrt{3}}{2})\)
Replace the s with \(\frac{2}{3}x\). Then:
\(2x = \frac{(\frac{2}{3} x)^2 \sqrt{3}}{2} = \frac{\frac{4}{9} x^2 \sqrt{3}}{2 }→ 4x = \frac{4}{9} x^2 \sqrt{3} → 4 = \frac{4}{9} x\sqrt{3} → 9 = x\sqrt{3}→
\frac{9}{\sqrt{3} }= x → \frac{9}{\sqrt{3} } × \frac{\sqrt{3}}{\sqrt{3} } = x → x = 3\sqrt{3}\)
Then, one side of the triangle is: \(\frac{2}{3}x =\frac{ 2}{3}(3\sqrt{3}) = 2\sqrt{3}\)
Related to This Article
More math articles
- How to Use Exponents to Write down Multiplication Expressions?
- CHSPE Math Worksheets: FREE & Printable
- Quadratic Function
- 8th Grade NSCAS Math Worksheets: FREE & Printable
- ISEE Middle Level Math FREE Sample Practice Questions
- Top 10 Tips to Overcome CHSPE Math Anxiety
- Full-Length GRE Math Practice Test-Answers and Explanations
- Getting Better at Math: Realistic Tips and Suggestions
- The Ultimate ALEKS Math Course (+FREE Worksheets & Tests)
- Best Calculator For 11th Grade Students
What people say about "Geometry Puzzle – Challenge 76 - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.