# Square

If we increase side of the square, increase its area of 63%.
What is the percentage we increase side of the square?

Correct result:

p =  27.7 %

#### Solution:

$S=a^2 \ \\ S(1+\dfrac{ 63}{100}) = (a(1+\dfrac{p}{100}))^2 \ \\ S \cdot 1.63 = (a(1+\dfrac{p}{100}))^2 \ \\ a^2\cdot 1.63 = (a(1+\dfrac{p}{100}))^2 \ \\ 1.63 = (1+\dfrac{p}{100})^2 \ \\ \sqrt{ 1.63} = 1+\dfrac{p}{100} \ \\ \sqrt{ 1.63 } -1 = \dfrac{p}{100} \ \\ 100(\sqrt{ 1.63 } -1) = p \ \\ 27.7 \% = p$

We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!

Tips to related online calculators
Do you want to convert length units?

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• Magnification of the square
If we increase the square side, increase the content of the 94 %. About what percentage was increased his sides?
• Property
The length of the rectangle-shaped property is 8 meters less than three times of the width. If we increase the width 5% of a length and lendth reduce by 14% of the width it will increase the property perimeter by 13 meters. How much will the property cost
• Expansion
If one side of the rectangle is larger 4-times and second 2-times, what percentage increases the area of rectangle?
• Square - increased perimeter
How many times is increased perimeter of the square, where its sides increases by 150%? If the perimeter of square will increase twice, how much% increases the content area of the square?
• Square
If the length of the sides of the square we decrease by 25% decrease the content area of 28 cm2. Determine the side length of the original square.
• Roof cover
Above the pavilion with a square ground plan with a side length of a = 12 m is a pyramid-shaped roof with a height v = 4.5 m. Calculate how much m2 of sheet metal is needed to cover this roof if 5.5% of the sheet we must add for joints and waste.
• Folding table
The folding kitchen table has a rectangular shape with an area of 168dm2 (side and is 14 dm long). If necessary, it can be enlarged by sliding two semi-circular plates (at sides b). How much percent will the table area increase? The result round to one-hu
• Square side
If we enlarge the square side a = 5m, its area will increase by 10,25%. How many percent will the side of the square increase? How many percent will it increase the circumference of the square?
• Percentage and rectangle
About what percentage increases perimeter and area of a rectangle if both the sides 12 cm and 10 cm long we increase by 20%?
• Plot
The length of the rectangle is 8 smaller than three times the width. If we increase the width by 5% of the length and the length is reduced by 14% of the width, the circumference of rectangle will be increased by 30 m. What are the dimensions of the recta
• Three shapes
1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle?
• Fence and scale
The garden with 80 m of fencing is draw on plan as a square with a side length of 4 cm. At what scale is this plan made?
• Ratio of sides 2
The ratio of the side lengths of one square to another is 1:2. Find the ratio of the area of the two squares.
• Hop-garden
The length of the rectangular hop garden Mr. Smith increased by 25% and its width by 30%. What is the percentage change in area of hop garden?
• Trapezoid - diagonal
Trapezoid has a length of diagonal AC corssed with diagonal BD in the ratio 2:1. The triangle created by points A, cross point of diagonals S and point D has area 164 cm2. What is the area of the trapezoid?
• Percent change
If the length of a rectangle is increased by 25% and the width is decreased by 10%, the area of the rectangle is larger than the area of the original rectangle by what percent?
• Black building
Keith built building with a rectangular shape 6.5 m × 3.9 m. Calculate how much percent exceeded the limit 25 m2 for small building. Building not built in accordance with the law is called "black building". Calculate the angle that the walls were clenchi