Catheti

The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.

Result

a =  40
b =  9

Solution:

c=41 a+b=49 a2+b2=c2=1681 (a+b)2=492 a2+2ab+b2=2401  2ab=24011681 2a(49a)=720 249a2a2=720  2a298a+720=0  p=2;q=98;r=720 D=q24pr=98242720=3844 D>0  a1,2=q±D2p=98±38444 a1,2=98±624 a1,2=24.5±15.5 a1=40 a2=9   Factored form of the equation:  2(a40)(a9)=0 c= 41 \ \\ a+b = 49 \ \\ a^2 + b^2 = c^2 = 1681 \ \\ (a+b)^2 = 49^2 \ \\ a^2+2ab+b^2 = 2401 \ \\ \ \\ 2ab = 2401-1681 \ \\ 2a(49-a) = 720 \ \\ 2\cdot 49 a - 2a^2 = 720 \ \\ \ \\ 2a^2 -98a +720 =0 \ \\ \ \\ p=2; q=-98; r=720 \ \\ D = q^2 - 4pr = 98^2 - 4\cdot 2 \cdot 720 = 3844 \ \\ D>0 \ \\ \ \\ a_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ 98 \pm \sqrt{ 3844 } }{ 4 } \ \\ a_{1,2} = \dfrac{ 98 \pm 62 }{ 4 } \ \\ a_{1,2} = 24.5 \pm 15.5 \ \\ a_{1} = 40 \ \\ a_{2} = 9 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 2 (a -40) (a -9) = 0 \ \\
b=a2=9b= a_2 = 9



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.

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. 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.
  2. Euclid2
    euclid In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
  3. ABS CN
    complex_num Calculate the absolute value of complex number -15-29i.
  4. RT and circles
    r_triangle Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23.
  5. Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  6. Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  7. Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  8. Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  9. Solve 3
    eq2_4 Solve quadratic equation: (6n+1) (4n-1) = 3n2
  10. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  11. Square root 2
    parabola_2 If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
  12. Evaluation of expressions
    eq222_10 If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3
  13. Cinema 4
    cinema_2 In cinema are 1656 seats and in the last row are 105 seats , in each next row 3 seats less. How many are the total rows in cinema?
  14. Tubes
    pipes_1 Iron tubes in the warehouse are stored in layers so that each tube top layer fit into the gaps of the lower layer. How many layers are needed to deposit 100 tubes if top layer has 9 tubes? How many tubes are in bottom layer of tubes?
  15. Variable
    eq2_12 Find variable P: PP plus P x P plus P = 160
  16. Equation with abs value
    abs_graph How many solutions has the equation ? in the real numbers?
  17. Reciprocal equation 2
    parabola2 Solve this equation: x + 5/x - 6 = 4/11