A rectangular patio

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.

Correct result:

c =  30 ft
d =  40 ft

Solution:

a=20 ft b=30 ft  (a+x)(b+x)=2ab  (20+x) (30+x)=2 20 30 x2+50x600=0  a=1;b=50;c=600 D=b24ac=50241(600)=4900 D>0  x1,2=b±D2a=50±49002 x1,2=50±702 x1,2=25±35 x1=10 x2=60   Factored form of the equation:  (x10)(x+60)=0  c=a+x1=20+10=30 ft

Our quadratic equation calculator calculates it.

d=b+x1=30+10=40 ft



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
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?

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:

  • Area of garden
    garden_20 If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increas
  • Rectangle
    obdlznik_torta Area of rectangle is 3002. Its length is 41 larger than the width. What are the dimensions of the rectangle?
  • The length
    rectangle_14 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.
  • Rectangle field
    land The field has a shape of a rectangle having a length of 119 m and a width of 19 m. , How many meters have to shorten its length and increase its width to maintain its area and circumference increased by 24 m?
  • Rectangle - area, perimeter
    rectnagles_2 The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.
  • The hall
    lucerna The hall had a rectangular ground plan one dimension 20 m longer than the other. After rebuilding the length of the hall declined by 5 m and the width has increased by 10 m. Floor area increased by 300 m2. What were the original dimensions of the hall?
  • Rectangular garden
    rectangle_1 The perimeter of Peter's rectangular garden is 98 meters. The width of the garden is 60% shorter than its length. Find the dimensions of the rectangular garden in meters. Find the garden area in square meters.
  • Rectangle
    rectangles_1 The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
  • Rectangle
    squares2_3 Calculate area of the rectangle if its length is 12 cm longer than its width and length is equal to the square of its width.
  • Diagonal 20
    plaza Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be?
  • Garden
    garden_6 The garden has a rectangular shape and has a circumference of 130 m and area 800.25 m2. Calculate the dimensions of the garden.
  • An architect
    tiles2_1 An architect makes a model of a new house. The model shows a tile patio in the backyard. In the model each tile has length of 1/2 inch and width of 1/6 inch. The actual tiles have length of 2/3 feet and width 2/9 feet. What is the ratio of the length of a
  • Rectangular plot
    rectangular plot The dimensions of a rectangular plot are (x+1)m and (2x-y)m. If the sum of x and y is 3m and the perimeter of the plot is 36m. Find the area of the diagonal of the plot.
  • Jared's room painting
    painter Jared wants to paint his room. The dimensions of the room are 12 feet by 15 feet, and the walls are 9 feet high. There are two windows that measure 6 feet by 5 feet each. There are two doors, whose dimensions are 30 inches by 6 feet each. If a gallon of p
  • Rectangular field
    rectangle_inside_circle_2 A rectangular field has a diagonal of length 169m. If the length and width are in the ratio 12:5. Find the dimensions of the field, the perimeter of the field and the area of the field.
  • Rectangle 35
    rectangles_13 Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length.
  • Plot
    rectangle_5 The length of the rectangle is 8 smaller than three times the width. If we increase the width by 5% of the length and the length is reduced by 14% of the width, the circumference of rectangle will be increased by 30 m. What are the dimensions of the recta