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!


Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
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:

  • Coordinates
    geodet Determine the coordinates of the vertices and the content of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0
  • 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.
  • Inclined plane
    naklonena_rovina 1. How much work W we have to do to pull a body weighing 200 kg along an inclined plane with a length of 4 m to a total height of 1.5 m. 2. Find the force we need to exert to do this if we neglect frictional resistance. 3. Find the force we would need i
  • 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.
  • Two chords
    ssa From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords.
  • 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?
  • The tower
    veza_huly The observer sees the base of the tower 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands?
  • Regular hexagonal prism
    hexagon_prism2 Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.
  • Traffic sign
    cyklo2 There is a traffic sign for climbing on the road with an angle of 7%. Calculate at what angle the road rises (falls).
  • Fighter
    vyskovy uhol A military fighter flies at an altitude of 10 km. From the ground position, it was aimed at an altitude angle of 23° and 12 seconds later at an altitude angle of 27°. Calculate the speed of the fighter in km/h.
  • The right triangle
    rt_triangle_1 In the right triangle ABC with right angle at C we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles.
  • Six questions test
    binomial_1 There are six questions in the test. There are 3 answers to each - only one is correct. In order for a student to take the exam, at least four questions must be answered correctly. Alan didn't learn at all, so he circled the answers only by guessing. What
  • Lookout tower
    tower How high is the lookout tower? If each step was 3 cm lower, there would be 60 more of them on the lookout tower. If it was 3 cm higher again, it would be 40 less than it is now.
  • 1 page
    books 1 page is torn from the book. The sum of the page numbers of all the remaining pages is 15,000. What numbers did the pages have on the page that was torn from the book?
  • Tournament
    futball_ball How many matches will be played in a football tournament in which there are two groups of 5 teams if one match is played in groups with each other and the group winners play a match for the overall winner of the tournament?
  • Finite arithmetic sequence
    seq_sum_1 How many numbers should be inserted between the numbers 1 and 25 so that all numbers create a finite arithmetic sequence and that the sum of all members of this group is 117?
  • Summands
    numbers_2 We want to split the number 110 into three summands so that the first and the second summand are in the ratio 4: 5, and the third with the first are in ratio 7: 3. Calculate the smallest of the summands.