# Geometry Puzzle – Challenge 69

Who can solve this math puzzle quickly? This is a great logic challenge for those who love critical thinking challenges. Let’s challenge your brain!

## Challenge:

A length of a rectangle is increased by $$20\%$$. What percent of its width should be decreased to keep the area of the rectangle the same?

A- $$15\%$$

B- $$16\frac{2}{3}\%$$

C- $$20\%$$

D- $$25\%$$

E- $$30\%$$

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The correct answer is B.

The area of a rectangle is the product of its width and length. Let x be the area of the rectangle.
Area of a rectangle = Width × Length = x
Length → 1.2Length → Area of a rectangle = Width × 1.2Length = x
Let W1 be the width of the first rectangle and W2 be the width of the second rectangle.
W1 × 1.2L = W2 × L → W1 × 1.2 = W2 → W1 $$= \frac{1}{1.2}$$W2 →
W1 $$= \frac{5}{6 }$$W2
To keep the area of the rectangle the same $$\frac{1}{6 }$$ or $$16\frac{2}{3}$$ percent of the width should be decreased.

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