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.
Reza is an experienced Math instructor and a test-prep expert who has been tutoring students since 2008. He has helped many students raise their standardized test scores--and attend the colleges of their dreams. He works with students individually and in group settings, he tutors both live and online Math courses and the Math portion of standardized tests. He provides an individualized custom learning plan and the personalized attention that makes a difference in how students view math.
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