Two gardens

The flower garden has a square shape. The new garden has the shape of a rectangle, and one dimension is 8 m smaller, and the other is twice as large as in a square garden. What were the original garden dimensions and the new garden if both gardens' area is the same?

Correct answer:

a =  16 m
x =  8 m
y =  32 m

Step-by-step explanation:

$$\begin{gathered} S_1=S_2 \\ {S}_1=a^2 \\ {S}_2=x\cdot y \\ x=a-8 \\ y=2a \\ {a}^2=x\cdot y \\ {a}^2=(a-8)\ast 2a \\ {a}^2=(a-8)\cdot 2a \\ -a^2+16a=0 \\ {a}^2-16a=0 \\ p=1;q=-16;r=0 \\ D=q^2-4pr=16^2-4\cdot 1\cdot 0=256 \\ D>0 \\ {a}_{1,2}={\displaystyle \frac{-q\pm \sqrt{D}}{2p}}={\displaystyle \frac{16\pm \sqrt{256}}{2}} \\ {a}_{1,2}={\displaystyle \frac{16\pm 16}{2}} \\ {a}_{1,2}=8\pm 8 \\ {a}_1=16 \\ {a}_2=0 \\ \text{ Factored form of the equation: } \\ (a-16)a=0 \\ a=a_1=16=16\text{ m} \end{gathered}$$

Our quadratic equation calculator calculates it.

$x=a-8=16-8=8\text{ m}$

$$\begin{gathered} y=2\cdot a=2\cdot 16=32=32\text{ m } \\ \text{ Verifying Solution: } \\ {S}_1=a^2=16^2=256{\text{m}}^2 \\ {S}_2=x\cdot y=8\cdot 32=256{\text{m}}^2 \end{gathered}$$

Try another example

Related math problems and questions:

• The width
  The width of a rectangular garden is 4 m less than the length. If the area of a rectangular garden is 96 square meters, what is the dimension of the garden?
• Two gardens
  The total area of the two gardens is 864 m². The first garden is 60 m² smaller than three times the second garden. What is the area of each garden?
• The hall
  The hall had a rectangular ground plan one dimension 20 m longer than the other. After rebuilding the length of the hall declined by 5 m and the width has increased by 10 m. Floor area increased by 300 m². What were the original dimensions of the hall?
• Square vs rectangle
  Square and rectangle have the same area contents. The length of the rectangle is 9 greater and width 6 less than side of the square. Calculate the side of a square.
• Garden
  The garden has a rectangular shape and has a circumference of 130 m and area 800.25 m². Calculate the dimensions of the garden.
• The pool
  The cube-shaped pool has 140 cubic meters of water. Determine the dimensions of the bottom if the depth of the water is 200 cm and one dimension of the bottom is 3 m greater than the other. What are the dimensions of the pool bottom?
• Extending square garden
  Mrs. Petrová's garden had the shape of a square with a side length of 15 m. After its enlargement by 64 m² (square), it had the shape of a square again. How many meters has the length of each side of the garden been extended?
• Flowerbed 2
  Around the square flower bed in a park is sidewalk 2 m wide. The area of ​​this sidewalk is 243 m². What is the area of the flowerbed?
• Gardens
  I have a garden in the shape of a square with a side length of 0.02 kilometers. Neighbor has a large garden as well and one side of the garden we share. I'd bought from a neighbor garden that my area of my garden increased to 5 ares. a/ By how many acres
• 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
• 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.
• Area and perimeter of rectangle
  The content area of the rectangle is 3000 cm², one dimension is 10 cm larger than the other. Determine the perimeter of the rectangle.
• Rectangular garden 2
  A farmer bought 600 m of wire for the fence. He wants to use it to besiege a rectangular garden with a surface of 16875 m². Calculate the size of the garden.
• Gardens
  The area of the square garden is 3/4 of the area of the triangular garden with sides of 80 m, 50 m, 50 m. How many meters of the fence do we need to fence a square garden?
• Gardens
  The garden has the square shape with circumference 124 m. Divide it into two rectangular gardens, one should circumference 10 meters more than the second. What size will have a gardens?
• Completing square
  Solve the quadratic equation: m²=4m+20 using completing the square method
• Trapezoid 15
  Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4