# Rectangle field

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?

Result

x =  102 m
y =  114 m

#### Solution:

$119 \cdot \ 19 = (119-x) \cdot \ (19+y) \ \\ 2(119+19) + 24 = 2 \cdot \ ((119-x)+(19+y)) \ \\ \ \\ y = x+12 \ \\ \ \\ \ \\ 119 \cdot \ 19 = (119-x) \cdot \ (19+(x+12)) \ \\ x^2 -88x -1428 = 0 \ \\ \ \\ a = 1; b = -88; c = -1428 \ \\ D = b^2 - 4ac = 88^2 - 4\cdot 1 \cdot (-1428) = 13456 \ \\ D>0 \ \\ \ \\ x_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 88 \pm \sqrt{ 13456 } }{ 2 } \ \\ x_{1,2} = \dfrac{ 88 \pm 116 }{ 2 } \ \\ x_{1,2} = 44 \pm 58 \ \\ x_{1} = 102 \ \\ x_{2} = -14 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -102) (x +14) = 0 \ \\ x = x_{ 1 } = 102 = 102 \ \text { m }$

Checkout calculation with our calculator of quadratic equations.

$y = x+12 = 102+12 = 114 \ \\ a = 119-x = 119-102 = 17 \ m \ \\ b = 19+y = 19+114 = 133 \ m \ \\ \ \\ y = 114 = 114 \ \text { m }$

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...):

Be the first to comment!

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

Looking for help with calculating roots of a quadratic equation? Do you have a system of equations and looking for calculator system of linear equations? Do you want to convert length units?

## Next similar math problems:

1. Rectangle - area, perimeter
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.
2. Area of rectangle
Calculate the area of rectangle in square meters whose sides have dimensions a = 80dm and b = 160dm.
3. Rectangle
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.
4. 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.
5. Rectangle - sides
What is the perimeter of a rectangle with area 266 cm2 if length of the shorter side is 5 cm shorter than the length of the longer side?
6. Interesting property
Plot a rectangular shape has the interesting property that circumference in meters and the area in square meters are the same numbers. What are the dimensions of the rectangle?
7. Rectangular garden 2
A farmer bought 600 m of wire for the fence. He wants to use it to besiege a rectangular garden with a surface of 16875 m2. Calculate the size of the garden.
8. Garden
The garden has a rectangular shape and has a circumference of 130 m and area 800.25 m2. Calculate the dimensions of the garden.
9. Table
The circumference of the rectangle table is 420 cm. Length to width ratio is 5:2 . Calculate table dimensions and dimensions reduced in the ratio 3:5
10. Trapezium
The lengths of a parallel sides of a trapezium are (2x+3) and (x+8) and the distance between them is (x+4). if the area of the trapezium is 590 , find the value of x.
11. Discriminant
Determine the discriminant of the equation: ?