Right-angled triangle

Determine the content of a right triangle whose side lengths form successive members of an arithmetic progression and the radius of the circle described by the triangle is 5 cm.

Correct answer:

S =  24 cm2

Step-by-step explanation:

r=5 cm c=2 r=2 5=10 cm c2=a2+b2 a=c2d b=cd c2=(c2d)2+(cd)2  102=(102d)2+(10d)2  5d2+60d100=0 5d260d+100=0  a=5;b=60;c=100 D=b24ac=60245100=1600 D>0  d1,2=b±D2a=60±160010 d1,2=60±4010 d1,2=6±4 d1=10 d2=2   Factored form of the equation:  5(d10)(d2)=0  d<c d=d2=2 b=cd=102=8 cm a=c2 d=102 2=6 cm S=a b/2=6 8/2=24 cm2

Our quadratic equation calculator calculates it.


Try calculation via our triangle calculator.




We will be pleased if You send us any improvements to this math problem. Thank you!



avatar




Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
See also our right triangle calculator.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions:

  • Rectangular triangle
    rt_triangle_2 The lengths of the rectangular triangle sides with a longer leg of 12 cm form an arithmetic sequence. What is the area of the triangle?
  • AP RT triangle
    right_triangle_4 The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
  • Circle and rectangle
    described_circle A rectangle with sides of 11.7 cm and 175 mm is described by circle. What is its length? Calculate the content area of the circle described by this circle.
  • Circle described
    described_circle_right_triangle The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
  • Right triangle
    rt_triangle_1 A circle with a radius of 5 cm is described in a right triangle with a 6 cm leg. What is the height at the hypotenuse of this triangle?
  • 30-gon
    30gon At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
  • Inscribed circle
    inscribed_circle XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm.
  • Cathethus and the inscribed circle
    RightTriangleInradius In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.
  • Square
    percent 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.
  • Diamond diagonals
    kosodlznik_2 Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
  • Diamond diagonals
    kosostvorec_9 Calculate the diamond's diagonal lengths if its content is 156 cm2 and the side length is 13 cm.
  • Square and rectangle
    ctverec 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.
  • Right angled triangle
    fun-triangle The hypotenuse of a right triangle is 17 cm long. When we decrease the length of legs by 3 cm, then decrease its hypotenuse by 4 cm. Find the size of its legs.
  • Isosceles trapezoid
    lichobeznik_5 Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high.
  • Perimeter and legs
    RT_triangle 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.
  • Two chords
    chords_1 In a circle with a radius of 8.5 cm, two parallel chords are constructed, the lengths of which are 9 cm and 12 cm. Find the distance of the chords in a circle.
  • Triangular pyramid
    3sidesPyramid It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm3. What is it content (surface area)?