# 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. Circular pool
The base of the pool is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool?
2. Area of a rectangle
Calculate the area of a rectangle with a diagonal of u = 12.5cm and a width of b = 3.5cm. Use the Pythagorean theorem.
3. Rectangle
In rectangle with sides, 6 and 3 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
4. Ratio of sides
Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles.
6. Rectangle
The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle.
7. Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
8. Garden
Area of a square garden is 6/4 of triangle garden with sides 56 m, 35 m, and 35 m. How many meters of fencing need to fence a square garden?
9. Trapezoid MO-5-Z8
ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm2. Determine the area of the trapezoid A
10. 30-gon
At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
11. Annular area
The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area.
12. The trapezium
The trapezium is formed by cutting the top of the right-angled isosceles triangle. The base of the trapezium is 10 cm and the top is 5 cm. Find the area of trapezium.
13. Triangle SAS
Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
14. Rhombus
Calculate the perimeter and area of ​​a rhombus whose diagonals are 39 cm and 51 cm long.
15. Square diagonal
Calculate the length of the square diagonal if the perimeter is 476 cm.
16. Rhombus
It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a1 = 14 cm and a2 = 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
17. Quarter circle
What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?