Diagonal of the rectangle

Calculate the rectangle's diagonal, which area is 54 centimeters square, and the circuit is equal to 30 cm.

Correct answer:

u =  10.8167

Step-by-step explanation:

$$\begin{gathered} S=54 \\ o=30 \\ S=a\cdot b \\ o=2\cdot (a+b) \\ S=a\cdot (o\mathrm{/}2-a) \\ 54=a\ast (30\mathrm{/}2-a) \\ 54=a\cdot (30\mathrm{/}2-a) \\ {a}^2-15a+54=0 \\ p=1;q=-15;r=54 \\ D=q^2-4pr=15^2-4\cdot 1\cdot 54=9 \\ D>0 \\ {a}_{1,2}={\displaystyle \frac{-q\pm \sqrt{D}}{2p}}={\displaystyle \frac{15\pm \sqrt{9}}{2}} \\ {a}_{1,2}={\displaystyle \frac{15\pm 3}{2}} \\ {a}_{1,2}=7.5\pm 1.5 \\ {a}_1=9 \\ {a}_2=6 \\ \text{ Factored form of the equation: } \\ (a-9)(a-6)=0 \\ a=a_1=9 \\ b=a_2=6 \\ u=\sqrt{a^2+b^2}=\sqrt{9^2+6^2}=3\sqrt{13}=10.8167 \end{gathered}$$

Our quadratic equation calculator calculates it.

Try another example

Related math problems and questions:

• Rectangle 35
  Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length.
• Rectangle
  There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of a rectangle.
• Uboid volume
  Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
• Body diagonal
  The cuboid has a volume of 32 cm³. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
• Diamond diagonals
  Calculate the diamond's diagonal lengths if its content is 156 cm² and the side length is 13 cm.
• 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.
• Diamond diagonals
  Find the diamond diagonal's lengths if the area is 156 cm² and side is 13 cm long.
• A rectangle 2
  A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.
• Diagonal to area
  Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
• Block or cuboid
  The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
• Square s3
  Calculate the diagonal of the square, where its area is 0.49 cm square. And also calculate its circumference.
• 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 rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.
• ISO trapezoid v2
  bases of Isosceles trapezoid measured 20 cm and 4 cm and its perimeter is 55 cm. What is the are of a trapezoid?
• Rectangle diagonals
  It is given a rectangle with an area of 24 cm² a circumference of 20 cm. The length of one side is 2 cm larger than the length of the second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
• Diamond diagonals
  Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square, and the side length is 13 cm.
• Rectangle diagonal
  The rectangle, one side of which is 5 cm long, is divided by a 13 cm diagonal into two triangles. Calculate the area of one of these triangles in cm².