Geometry Puzzle – Challenge 76

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 "Geometry Puzzle – Challenge 76"

Other Topics Puzzle – Challenge 100
Other Topics Puzzle – Challenge 100
Other Topics Puzzle – Challenge 99
Other Topics Puzzle – Challenge 99
Other Topics Puzzle – Challenge 98
Other Topics Puzzle – Challenge 98
Other Topics Puzzle – Challenge 97
Other Topics Puzzle – Challenge 97
Other Topics Puzzle – Challenge 96
Other Topics Puzzle – Challenge 96
Other Topics Puzzle – Challenge 95
Other Topics Puzzle – Challenge 95
Other Topics Puzzle – Challenge 94
Other Topics Puzzle – Challenge 94
Intelligent Math Puzzle – Challenge 93
Intelligent Math Puzzle – Challenge 93
Intelligent Math Puzzle – Challenge 92
Intelligent Math Puzzle – Challenge 92
Intelligent Math Puzzle – Challenge 91
Intelligent Math Puzzle – Challenge 91

Leave a Reply

Your email address will not be published. Required fields are marked *

27% OFF

Download Instantly

X

How Does It Work?

Find Books

1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.

add to cart

2. Add to Cart

Add the eBook to your cart.

checkout

3. Checkout

Complete the quick and easy checkout process.

download

4. Download

Immediately receive the download link and get the eBook in PDF format.

Why Buy eBook From Effortlessmath?

Save money

Save up to 70% compared to print

Instantly download

Instantly download and access your eBook

help environment

Help save the environment

Access

Lifetime access to your eBook

Test titles

Over 2,000 Test Prep titles available

Customers

Over 80,000 happy customers

Star

Over 10,000 reviews with an average rating of 4.5 out of 5

Support

24/7 support

Anywhere

Anytime, Anywhere Access

Find Your Test

Schools, tutoring centers, instructors, and parents can purchase Effortless Math eBooks individually or in bulk with a credit card or PayPal. Find out more…