Euclid1

Right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?

Correct result:

c1 =  26.66 cm
c2 =  0.34 cm

Solution:

c1+c2=27 c1c2=32   x227x+9=0  a=1;b=27;c=9 D=b24ac=272419=693 D>0  x1,2=b±D2a=27±6932=27±3772 x1,2=13.5±13.1624465811 x1=26.6624465811 x2=0.337553418912   Factored form of the equation:  (x26.6624465811)(x0.337553418912)=0  c1=26.66 cmc_1+c_2 = 27 \ \\ c_1 \cdot c_2 = 3^2 \ \\ \ \\ \ \\ x^2 -27x +9 =0 \ \\ \ \\ a=1; b=-27; c=9 \ \\ D = b^2 - 4ac = 27^2 - 4\cdot 1 \cdot 9 = 693 \ \\ D>0 \ \\ \ \\ x_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 27 \pm \sqrt{ 693 } }{ 2 } = \dfrac{ 27 \pm 3 \sqrt{ 77 } }{ 2 } \ \\ x_{1,2} = 13.5 \pm 13.1624465811 \ \\ x_{1} = 26.6624465811 \ \\ x_{2} = 0.337553418912 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -26.6624465811) (x -0.337553418912) = 0 \ \\ \ \\ c_1 = 26.66 \ \text{cm}
c2=0.34 cm

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
Looking for help with calculating roots of 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

Next similar math problems:

  • Hypotenuse and height
    euklides In a right triangle is length of the hypotenuse c = 56 cm and height hc = 4 cm. Determine the length of both trangle legs.
  • Euclid theorems
    euklidova_veta_trojuhelnik_nakres Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm.
  • Right Δ
    ruler A right triangle has the length of one leg 11 cm and length of the hypotenuse 61 cm. Calculate the height of the triangle.
  • Without Euclid laws
    euclid_1 Right triangle ABC with right angle at the C has a=5 and hypotenuse c=19. Calculate the height h of this triangle without the use of Euclidean laws.
  • Area of RT
    sandwich_rt In the right triangle has orthogonal projections of legs to the hypotenuse lengths 7 cm and 12 cm. Determine the area of ​​this triangle.
  • Euclid 5
    euclid_3 Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
  • 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 - hypotenuse and altitude
    pravy_trojuholnik Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments?
  • Area of RT
    right_triangle_sepia Calculate the area of a right triangle that hypotenuse has length 14, and one hypotenuse segment has length 5.
  • Right triangle - ratio
    rt_triangle The lengths of the legs of the right triangle ABC are in ratio b = 2: 3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle.
  • Triangle KLM
    klm_triangle In the rectangular triangle KLM, where is hypotenuse m (sketch it!) find the length of the leg k and the height of triangle h if hypotenuse's segments are known mk = 5cm and ml = 15cm
  • Hypotenuse - RT
    triangle_bac_1 A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
  • 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.
  • RTriangle 17
    rt The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm you will reduce the hypotenuse by 4 cm. Determine the length of this legs.
  • Leg and height
    right_triangles Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m.
  • Right triangle
    righttriangle 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.
  • 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?