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.

Correct result:

a =  18

Solution:

$$\begin{gathered} S_1=S_2 \\ {a}^2=(a+9)(a-6) \\ {a}^2=a^2+9a-6a-9\cdot 6 \\ 3a=9\cdot 6=18 \\ a=9\cdot 6\mathrm{/}3=18 \\ {S}_1=a^2=18^2=324 \\ {S}_2=(a+9)\cdot (a-6)=(18+9)\cdot (18-6)=324 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Uboid volume
  Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
• Rectangle vs square
  One side of the rectangle is 1 cm shorter than the side of the square, the second side is 3 cm longer than the side of the square. Square and rectangle have the same content. Calculate the length of the sides of a square and a rectangle.
• Rectangle diagonals
  It is given rectangle with area 24 cm² a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
• Rectangle
  Area of rectangle is 3002. Its length is 41 larger than the width. What are the dimensions of the rectangle?
• Square and rectangle
  Calculate the side of a square which content area equals area of the rectangle having a length of 3 cm greater and by 2 cm smaller than the side of the square.
• Rectangle
  Calculate area of the rectangle if its length is 12 cm longer than its width and length is equal to the square of its width.
• Rectangle
  The length of the rectangle is 12 cm greater than 3 times its width. What dimensions and area this rectangle has if ts circumference is 104 cm.
• Rectangle
  There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle.
• 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.
• Squares ratio
  The first square has a side length of a = 6 cm. The second square has a circumference of 6 dm. Calculate the proportions of the perimeters and the proportions of the contents of these squares? (Write the ratio in the basic form). (Perimeter = 4 * a, conte
• Pyramid
  The pyramid has a base rectangle with a = 6cm, b = 8cm. The side edges are the same and their length = 12.5 cm. Calculate the surface of the pyramid.
• The length
  The length of a rectangle is 6 meters less than twice the width. If the area of the rectangle is 216 meters, find the dimensions of the rectangle.
• Similarity of squares
  The ratio of the similarity of the squares ABCD and KLMN is 2.5. Square KLMN area is greater than area of a square ABCD with side a: ?
• In the
  In the rectangle ABCD, the distance of its center from the line AB is 3 cm greater than from the line BC. The circumference of the rectangle is 52 cm. Calculate the contents of the rectangle. Express the result in cm².
• Floating barrel
  Barrel (cylinder shape) floats on water, top of the barrel is 8 dm above water, and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel.
• Cuboid and ratio
  Cuboid has dimensions in ratio 1:2:6 and the surface area of the cuboid is 1000 dm². Calculate the volume of the cuboid.
• Diamond diagonals
  Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square, and the side length is 13 cm.