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.

Correct result:

u =  7.2111 cm

Solution:

$$\begin{gathered} S=24 \\ o=20 \\ S=ab \\ o=2(a+b) \\ b=10-a \\ 24=a\ast (10-a) \\ 24=a\cdot (10-a) \\ {a}^2-10a+24=0 \\ p=1;q=-10;r=24 \\ D=q^2-4pr=10^2-4\cdot 1\cdot 24=4 \\ D>0 \\ {a}_{1,2}={\displaystyle \frac{-q\pm \sqrt{D}}{2p}}={\displaystyle \frac{10\pm \sqrt{4}}{2}} \\ {a}_{1,2}={\displaystyle \frac{10\pm 2}{2}} \\ {a}_{1,2}=5\pm 1 \\ {a}_1=6 \\ {a}_2=4 \\ \text{ Factored form of the equation: } \\ (a-6)(a-4)=0 \\ a=a_1=6 \\ b=10-a=10-6=4 \\ u=\sqrt{a^2+b^2}=\sqrt{6^2+4^2}=2\sqrt{13}=7.2111\text{ cm} \end{gathered}$$

Our quadratic equation calculator calculates it.

Try another example

Showing 0 comments:

Next similar math problems:

• Ratio of sides
  Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
• 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.
• Right triangle
  Legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
• The field
  The player crossed the field diagonally and walked the length of 250 m. Calculate the length of the field, circumference if one side of field 25 meters.
• Right triangle eq2
  Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
• Rectangle
  The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle.
• 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.
• Diamond diagonals
  Calculate the diamond's diagonal lengths if its content is 156 cm² and the side length is 13 cm.
• Rectangular garden
  The sides of the rectangular garden are in ratio 1: 2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden.
• ISO triangle
  Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 377 mm.
• Right triangle eq2
  Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
• Diamond diagonals
  Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm.
• Rectangle
  The perimeter of the rectangle is 22 cm and content area 30 cm². Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
• Isosceles triangle 9
  Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm and altitude is 24cm. Find the area of the isosceles triangle
• Rectangular field
  A rectangular field has a diagonal of length 169m. If the length and width are in the ratio 12:5. Find the dimensions of the field, the perimeter of the field and the area of the field.
• 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.
• Diagonals
  Given a rhombus ABCD with a diagonalsl length of 8 cm and 12 cm. Calculate the side length and content of the rhombus.