RT sides

Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.

Correct result:

c =  13 cm
a =  12 cm
b =  5 cm

Solution:

a+b=17 r=2 cm  r=a+bc2  a+b=c+2r  c=172 r=172 2=13 cma+b=17 \ \\ r=2 \ \text{cm} \ \\ \ \\ r=\dfrac{ a+b-c }{ 2 } \ \\ \ \\ a+b=c+2r \ \\ \ \\ c=17 - 2 \cdot \ r=17 - 2 \cdot \ 2=13 \ \text{cm}
a2+b2=c2 a2+(17a)2=132  2a234a+120=0  p=2;q=34;r=120 D=q24pr=34242120=196 D>0  a1,2=q±D2p=34±1964 a1,2=34±144 a1,2=8.5±3.5 a1=12 a2=5   Factored form of the equation:  2(a12)(a5)=0  a=a1=12 cma^2+b^2=c^2 \ \\ a^2 + (17-a)^2=13^2 \ \\ \ \\ 2a^2 -34a +120=0 \ \\ \ \\ p=2; q=-34; r=120 \ \\ D=q^2 - 4pr=34^2 - 4\cdot 2 \cdot 120=196 \ \\ D>0 \ \\ \ \\ a_{1,2}=\dfrac{ -q \pm \sqrt{ D } }{ 2p }=\dfrac{ 34 \pm \sqrt{ 196 } }{ 4 } \ \\ a_{1,2}=\dfrac{ 34 \pm 14 }{ 4 } \ \\ a_{1,2}=8.5 \pm 3.5 \ \\ a_{1}=12 \ \\ a_{2}=5 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 2 (a -12) (a -5)=0 \ \\ \ \\ a=a_{1}=12 \ \text{cm}

Checkout calculation with our calculator of quadratic equations.

b=17a=1712=5 cmb=17-a=17-12=5 \ \text{cm}

Try calculation via our triangle calculator.




Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:
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 quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

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

Next similar math problems:

  • Hexagonal pyramid
    hexa_pyramid Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm.
  • Integer sides
    rt_triangle_1 A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side?
  • Right angle
    rt_triangle_1 In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle.
  • Triangle in a square
    stvorec In a square ABCD with side a = 6 cm, point E is the center of side AB and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides.
  • Find the 13
    circle_inside_rhombus Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4].
  • Hexagonal pyramid
    hexa_pyramid Find the area of a shell of the regular hexagonal pyramid, if you know that its base edge is 5 cm long and the height of this pyramid is 10 cm.
  • Quadrilateral pyramid
    jehlan_2 A regular quadrilateral pyramid has a volume of 24 dm3 and a base edge a = 4 dm. Calculate: a/height of the pyramid b/sidewall height c/surface of the pyramid
  • Truncated cone 6
    frustum-of-a-right-circular-cone Calculate the volume of the truncated cone whose bases consist of an inscribed circle and a circle circumscribed to the opposite sides of the cube with the edge length a=1.
  • Triangular prism
    prism3_1 The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm3? And the surface cm2?
  • The regular
    hranol3b The regular triangular prism has a base in the shape of an isosceles triangle with a base of 86 mm and 6.4 cm arms, the height of the prism is 24 cm. Calculate its volume.
  • Calculate 6
    distance_point_line Calculate the distance of a point A[0, 2] from a line passing through points B[9, 5] and C[1, -1].
  • Sailboat
    Plachetnice The 20 m long sailboat has an 8 m high mast in the middle of the deck. The top of the mast is fixed to the bow and stern with a steel cable. Determine how much cable is needed to secure the mast and what angle the cable will make with the ship's deck.
  • An observer
    tower An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower?
  • Trip with compass
    compass2 During the trip, Peter went 5 km straight north from the cottage, then 12 km west and finally returned straight to the cottage. How many kilometers did Peter cover during the whole trip?
  • Regular hexagonal prism
    hexagon_prism2 Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.
  • Sailing
    ship_2 Solve the following problem graphically. The fishing boat left the harbor early in the morning and set out to the north. After 12 km of sailing, she changed course and continued 9 km west. Then she docked and launched the nets. How far was she from the pl
  • On a line
    linearna On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1].