Geometry Puzzle – Challenge 65
If a square's side increases by 20%, by what percent does the area increase? Areas scale by the square of the linear scale factor. New side = 1.2 times original. New area = (1.2)^2 = 1.44 times original. That is a 44% increase.
Key takeaways:
- For a square, area = side^2.
- If side scales by factor k, area scales by k^2.
- Side scaled by 1.20 (20% increase) gives area scaled by 1.44, a 44% increase.
- This is the general rule for 2D area; for 3D volume the factor is k^3.
- Always check the relationship between linear and area/volume scaling.
Who can solve this math puzzle? This is a great math and critical thinking challenge to help you develop your creative thinking! For additional educational resources
Challenge:
If a side of a square is increased by \(20\%\), what percent of the area of the square will be increased?
A- \(20\%\)
B- \(40\%\)
C- \(44\%\)
D- \(100\%\)
E- \(200\%\)
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The correct answer is C.
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Area of a square = side times side.
Let X be the side of a square. Then, the side of the square is \(X^2\).
If a side of a square is increased by \(20\%\), then the area of the square will be increased by 44 percent:
\(1.2X × 1.2X = 1.44X^2\)
\(1.44X^2\) is 0.44 or \(44\%\) bigger than \(X^2\)The Best Books to Ace Algebra
Frequently Asked Questions
If one side of a square is increased by 20 percent, how much does the area increase?
The area increases by 44%. Each side becomes 1.2 times as long, and area uses side × side, so the new area is 1.2 × 1.2 = 1.44 times the old one. Check with numbers: a square with side 10 has area 100, and a side of 12 gives area 144, which is 44 more than 100.
If the side of a square is increased by 10%, what is the increase in area?
The area increases by 21%. The new side is 1.1 times the old side, so the new area is 1.1² = 1.21 times the original. With a side of 10, the area goes from 100 to 11 × 11 = 121. That is the same squaring rule used in the 20% puzzle, where 1.2² gives 1.44.
If the side length of a square is increased by 50%, by what percent is the area increased?
The area increases by 125%. A 50% increase multiplies the side by 1.5, and 1.5² = 2.25, so the new area is 2.25 times the original, or 125% more. A square with side 4 has area 16; with side 6 the area is 36, and 20 out of 16 is 125%.
How does the area of a square increase when its side increases?
The area grows by the square of the scale factor. If the side is multiplied by k, the area is multiplied by k². Doubling the side (k = 2) makes the area 4 times as large, a 300% increase. That is why a 20% longer side gives a 44% larger area, not 40%: the increase applies to both length and width.
Related Lessons You May Like
- How to find the area of rectangles
- How to find the perimeter of rectangles
- How to solve angles and angle measure
- How to solve percent of change
- How to find volume and surface area of cubes
If your student enjoys puzzles like this, Geometry for Beginners works the same kinds of relationships inside a full curriculum. Pre-Algebra for Beginners covers the algebraic foundations.
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