Sides of the triangle

Calculate triangle sides where its area is S = 84 cm2 and a = x, b = x + 1, xc = x + 2

Correct result:

a =  13 cm
b =  14 cm
c =  15 cm

Solution:

S=s(sa)(sb)(sc)=84 s=(a+b+c)/2=(3x+3)/2=1.5x+1.5 (1.5x+1.5)(1.5x+1.5x)(1.5x+1.5x1)(1.5x+1.5x2)=842 (1.5x+1.5)(0.5x+1.5)(0.5x+0.5)(0.5x0.5)=7056  0.1875x4+0.75x3+0.375x20.75x7056.56=0  x=13 a=x=13 cm 
b=13+1=14 cm
c=13+2=15 cm

Equation is non-linear.
Equation is not quadratic.
Equation is not cubic.

The real roots of the equation:

x1 = -14.9999987727
x2 = 12.9999987727

Our simple equation calculator calculates it.

Try calculation via our triangle calculator.




We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
avatar




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

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Next similar math problems:

  • RT 10
    triangles_rt Area of right triangle is 84 cm2 and one of its cathethus is a=10 cm. Calculate perimeter of the triangle ABC.
  • R Trapezium
    Trapezium_example Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
  • Isosceles triangle 9
    iso_triangle Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm, and the altitude is 24cm. Find the area of the isosceles triangle.
  • Euclid3
    euclid2 Calculate height and sides of the right triangle, if one leg is a = 81 cm and section of hypotenuse adjacent to the second leg cb = 39 cm.
  • RT triangle and height
    345 Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm.
  • Circles 2
    zlozite_kruznice Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 12 cm, 14 cm, 18 cm.
  • Right triangle Alef
    r_triangle The obvod of a right triangle is 84 cm, and the hypotenuse is 37 cm long. Determine the lengths of the legs.
  • Sides ratio
    triangle3_1 Calculate the circumference of a triangle with area 84 cm2 if a:b:c = 10:17:21
  • Right 24
    euclid_theorem Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 unequal segments. The length of one segment is 5 cm. What is the area of the triangle? Thank you.
  • Four circles
    circles_2 1) Calculate the circle radius if its area is 400 cm square 2) Calculate the radius of the circle whose circumference is 400 cm. 3) Calculate circle circumference if its area is 400 cm square 4) Calculate the circle's area if perimeter 400 cm.
  • Rhombus and inscribed circle
    rhombus_2 It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.
  • RT sides
    described_circle_right_triangle Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
  • Right isosceles triangle
    euclid_theorem_1 Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 equal segments. The length of one segment is 5 cm. What is the area of the triangle?
  • Triangle SAS
    triangle_iron Calculate the triangle area and perimeter, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
  • Squares above sides
    pataVysky Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm2. The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc
  • Four sides of trapezoid
    lichobeznik Calculate the area of the ABCD trapezoid with sides a = 65 cm, b = 29 cm, c = 40 cm, d = 36 cm
  • Diagonals of a rhombus 2
    rhombus3_4 One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm2, find the side of the rhombus.