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?

Correct answer:

p₁ =  5 %
p₂ =  5 %

Step-by-step explanation:

$$\begin{gathered} a=5\text{ m } \\ q=1+{\displaystyle \frac{10.25}{100}}={\displaystyle \frac{441}{400}}=1.1025 \\ S=a^2=5^2=25{\text{m}}^2 \\ {S}_1=q\cdot S=1.1025\cdot 25={\displaystyle \frac{441}{16}}=27.5625{\text{m}}^2 \\ {a}_1=\sqrt{S_1}=\sqrt{27.5625}={\displaystyle \frac{21}{4}}=5.25 \\ {p}_1=100\cdot {\displaystyle \frac{a_1-a}{a}}=100\cdot {\displaystyle \frac{5.25-5}{5}}=5\mathrm{\%} \end{gathered}$$

$$\begin{gathered} o=4\cdot a=4\cdot 5=20\text{ m } \\ {o}_1=4\cdot a_1=4\cdot 5.25=21\text{ m } \\ {p}_2=100\cdot {\displaystyle \frac{o_1-o}{o}}=100\cdot {\displaystyle \frac{21-20}{20}}=5\mathrm{\%} \end{gathered}$$

Try another example

Related math problems and questions:

• Square
  Suppose the square's sides' length decreases by a 25% decrease in the content area of 28 cm². Determine the side length of the original square.
• 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
• 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
• 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 we increase side of the square, increase its area of 63%. What is the percentage we increase side of the square?
• 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?
• Find the
  Find the number x, which if it increases by 2, then its square increases by 21 percent.
• Square sides
  If the square side increases by 28%, the square circumference increases by 11.2 meters. Find the length of the original square side.
• Perimeter and legs
  Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm².
• The number 72
  The number 72 increase by 25%. By how much % will you have to reduce the number you created to get the number 72 again?
• 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.
• Trapezoid
  trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area?
• Volume of wood
  Every year, at the same time, an increase in the volume of wood in the forest is measured. The increase is regularly p% compared to the previous year. If in 10 years the volume of wood has increased by 10%, what is the number p?
• Area of garden
  If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increas
• Rectangle field
  The field has a shape of a rectangle having a length of 119 m and a width of 19 m. , How many meters have to shorten its length and increase its width to maintain its area and circumference increased by 24 m?
• Stock market
  Simon one day decided to invest € 62000 to the stock market. After six months, he invested July 25 stock markets fell by 47%. Fortunately for Simon, from July 25 5 to October 25 his shares have risen by 39%. Simon is then: ...
• 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