The length

The length of a rectangle is 6 meters less than twice the width. If the area of the rectangle is 216 meters, find the dimensions of the rectangle.


a =  18 m
b =  12 m


a=2b6 S=ab=216  a(a+6)/2=216  0.5a2+3a216=0  p=0.5;q=3;r=216 D=q24pr=3240.5(216)=441 D>0  a1,2=q±D2p=3±4411=3±211 a1,2=3±21 a1=18 a2=24   Factored form of the equation:  0.5(a18)(a+24)=0  a=a1=18 ma=2b -6 \ \\ S=ab=216 \ \\ \ \\ a(a+6)/2=216 \ \\ \ \\ 0.5a^2 +3a -216=0 \ \\ \ \\ p=0.5; q=3; r=-216 \ \\ D=q^2 - 4pr=3^2 - 4\cdot 0.5 \cdot (-216)=441 \ \\ D>0 \ \\ \ \\ a_{1,2}=\dfrac{ -q \pm \sqrt{ D } }{ 2p }=\dfrac{ -3 \pm \sqrt{ 441 } }{ 1 }=-3 \pm 21 \sqrt{ 1 } \ \\ a_{1,2}=-3 \pm 21 \ \\ a_{1}=18 \ \\ a_{2}=-24 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 0.5 (a -18) (a +24)=0 \ \\ \ \\ a=a_{1}=18 \ \text{m}

Checkout calculation with our calculator of quadratic equations.

b=(a+6)/2=(18+6)/2=12 mb=(a+6)/2=(18+6)/2=12 \ \text{m}

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!

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?

You need to know the following knowledge to solve this word math problem:

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

Next similar math problems:

  1. A rectangular patio
    rectangles A rectangular patio measures 20 ft by 30 ft. By adding x feet to the width and x feet to the length, the area is doubled. Find the new dimensions of the patio.
  2. Water reservoir
    water_tower The cuboid reservoir contains 1900 hectoliters of water and the water height is 2.5 m. Determine the dimensions of the bottom where one dimension is 3.2 m longer than the second one.
  3. Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  4. Expression with powers
    eq222_9 If x-1/x=5, find the value of x4+1/x4
  5. Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  6. 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
  7. Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  8. Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  9. 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?
  10. Solve 3
    eq2_4 Solve quadratic equation: (6n+1) (4n-1) = 3n2
  11. Birthdays
    bonbons_1 In the classroom, students always give candy to their classmates on their birthdays. The birthday person always gives each one candy, and he does not give himself. A total of 650 candies were distributed in the class per year. How many students are in the
  12. Fraction
    polynomial For what x expression ? equals zero?
  13. Equation with abs value
    abs_graph How many solutions has the equation ? in the real numbers?
  14. Quadratic equation
    Parabola_tangent Quadratic equation ? has roots x1 = -26 and x2 = -86. Calculate the coefficients b and c.
  15. Variation equation
    fun2_4 Solve combinatorics equation: V(2, x+8)=72
  16. Quadratic equation
    parabola_1 Solve quadratic equation: 2x2-58x+396=0
  17. 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?