A rectangle 2

A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.

Result

a =  63.454 cm
b =  38.072 cm

Solution:

d=74 cm a:b=5:3  d2=a2+b2 b=35a d2=a2+(35a)2  a2=d2/(1+3252)  a=d1+3252=741+325263.4545=63.454  cm d = 74 \ cm \ \\ a:b = 5:3 \ \\ \ \\ d^2 = a^2 + b^2 \ \\ b = \dfrac{ 3 }{ 5 } a \ \\ d^2 = a^2 + (\dfrac{ 3 }{ 5 } a)^2 \ \\ \ \\ a^2 = d^2 / (1 + \dfrac{ 3^2 }{ 5^2 } ) \ \\ \ \\ a = \dfrac{ d }{ \sqrt{ 1 + \dfrac{ 3^2 }{ 5^2 } } } = \dfrac{ 74 }{ \sqrt{ 1 + \dfrac{ 3^2 }{ 5^2 } } } \doteq 63.4545 = 63.454 \ \text { cm }
b=35 a=35 63.4545=38.0724=38.072  cm   k=a/b=63.4545/38.0724=531.6667  d2=a2+b2=63.45452+38.0724273.9994 cmb = \dfrac{ 3 }{ 5 } \cdot \ a = \dfrac{ 3 }{ 5 } \cdot \ 63.4545 = 38.0724= 38.072 \ \text { cm } \ \\ \ \\ k = a/b = 63.4545/38.0724 = \dfrac{ 5 }{ 3 } \doteq 1.6667 \ \\ \ \\ d_{ 2 } = \sqrt{ a^2+b^2 } = \sqrt{ 63.4545^2+38.0724^2 } \doteq 73.9994 \ cm



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




Looking for help with calculating roots of a quadratic equation? Pythagorean theorem is the base for the right triangle calculator.

Next similar math problems:

  1. Tv screen
    tv2 The size of a tv screen is given by the length of its diagonal. If the dimension of a tv screen is 16 inches by 14 inches, what is the size of the tv screen?
  2. Diagonal of the rectangle
    rectangle_1 Calculate the diagonal of the rectangle which area is 54 centimeters square and the circuit is equal to 30 cm.
  3. Isosceles triangle
    triangle2_3 The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z.
  4. Algebra
    parabol_3 X+y=5, find xy (find the product of x and y if x+y = 5)
  5. Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  6. Expression with powers
    eq222_9 If x-1/x=5, find the value of x4+1/x4
  7. Power
    power Number ?. Find the value of x.
  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. Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  10. Calculation
    pocty How much is sum of square root of six and the square root of 225?
  11. Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  12. Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  13. Quadratic equation
    parabola_1 Solve quadratic equation: 2x2-58x+396=0
  14. 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?
  15. Product
    floring The product of two consecutive odd numbers is 8463. What are this numbers?
  16. Unknown number 7
    graph-parabola Calculate unknown number whose 12th power when divided by the 9th power get a number 27 times greater than the unknown number. Determine the unknown number.
  17. Completing square
    eq2_5 Solve the quadratic equation: m2=4m+20 using completing the square method