Right triangle eq2

Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.

Result

o =  -2 cm
S =  6 cm2

Solution:

c=9+a c=8+b c2=a2+b2   c2+34c145=0 c234c+145=0  p=1;q=34;r=145 D=q24pr=34241145=576 D>0  c1,2=q±D2p=34±5762 c1,2=34±242 c1,2=17±12 c1=29 c2=5   Factored form of the equation:  (c29)(c5)=0  c>9 c=c2=5 a=c9=59=4 b=c8=58=3 o=a+b+c=(4)+(3)+5=2 cmc=9+a \ \\ c=8+b \ \\ c^2=a^2+b^2 \ \\ \ \\ \ \\ -c^2 +34c -145=0 \ \\ c^2 -34c +145=0 \ \\ \ \\ p=1; q=-34; r=145 \ \\ D=q^2 - 4pr=34^2 - 4\cdot 1 \cdot 145=576 \ \\ D>0 \ \\ \ \\ c_{1,2}=\dfrac{ -q \pm \sqrt{ D } }{ 2p }=\dfrac{ 34 \pm \sqrt{ 576 } }{ 2 } \ \\ c_{1,2}=\dfrac{ 34 \pm 24 }{ 2 } \ \\ c_{1,2}=17 \pm 12 \ \\ c_{1}=29 \ \\ c_{2}=5 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (c -29) (c -5)=0 \ \\ \ \\ c>9 \ \\ c=c_{2}=5 \ \\ a=c-9=5-9=-4 \ \\ b=c-8=5-8=-3 \ \\ o=a+b+c=(-4)+(-3)+5=-2 \ \text{cm}

Checkout calculation with our calculator of quadratic equations.

S=a b/2=(4) (3)/2=6 cm2S=a \cdot \ b/2=(-4) \cdot \ (-3)/2=6 \ \text{cm}^2



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?
See also our trigonometric triangle calculator.
Pythagorean theorem is the base for the right triangle calculator.

Next similar math problems:

  1. Equilateral triangle v2
    eq_triangle Equilateral triangle has a perimeter 36 dm. What is its area?
  2. Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  3. Fifth of the number
    numbs_5 The fifth of the number is by 24 less than that number. What is the number?
  4. Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  5. Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  6. Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  7. Expression with powers
    eq222_9 If x-1/x=5, find the value of x4+1/x4
  8. 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?
  9. Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
  10. Algebra
    parabol_3 X+y=5, find xy (find the product of x and y if x+y = 5)
  11. Solve 3
    eq2_4 Solve quadratic equation: (6n+1) (4n-1) = 3n2
  12. Evaluation of expressions
    eq222_10 If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3
  13. Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  14. Fraction
    polynomial For what x expression ? equals zero?
  15. The product
    eq222 The product of a number plus that number and its inverse is two and one-half. What is the inverse of this number
  16. Square root 2
    parabola_2 If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
  17. Equation 23
    reciprocal_1 Find value of unknown x in equation: x+3/x+1=5 (problem finding x)