Rectangle

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.

Result

a =  5 cm
b =  6 cm

Solution:


a=1; b=11-a=10; S = ab=10
a=2; b=11-a=9; S = ab=18
a=3; b=11-a=8; S = ab=24
a=4; b=11-a=7; S = ab=28
a=5; b=11-a=6; S = ab=30 <<<<<< OK
a=6; b=11-a=5; S = ab=30 <<<<<< OK
a=7; b=11-a=4; S = ab=28
a=8; b=11-a=3; S = ab=24
a=9; b=11-a=2; S = ab=18
a=10; b=11-a=1; S = ab=10

The equations have the following integer solutions:
2(a+b)=22
ab = 30
a1=5, b1=6
a2=6, b2=5

Number of solutions found: 2

Calculated by our Diofant problems and integer equations.

Try another example






Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




To solve this example are needed these knowledge from mathematics:

Looking for help with calculating roots of a quadratic equation? Do you solve Diofant problems and looking for a calculator of Diofant integer equations?

Next similar examples:

  1. Rectangle - sides
    colored_squares 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?
  2. The rectangle
    rectangles_6 Determine the area of the rectangle where the length and width are in the ratio 5:2 and its length is 7.5 cm longer than its width. Determine also its length and its width.
  3. Enlarged rectangle
    rectangle_10 The rectangle with dimensions of 8 cm and 12 cm is enlarged in a ratio of 5:4. What are the circumference and the area of the enlarged rectangle?
  4. 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.
  5. Percentage and rectangle
    obdelnik2 About what percentage increases perimeter and area of a rectangle if both the sides 12 cm and 10 cm long we increase by 20%?
  6. Rectangle - sides 4
    mouse Perimeter of the rectangle is 72 cm. Calculate the length of the sides that are in the ratio 3:5.
  7. Rectangle
    obdlznik_torta Area of rectangle is 3002. Its length is 41 larger than the width. What are the dimensions of the rectangle?
  8. Folded square
    square_folded ABCD is a square. The square is folded on the midpoint of AB and A is folded onto the fold, creating a shaded region. The perimiter of the shaded figure is 75. Find the area of square ABCD
  9. Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  10. Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  11. Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  12. Theorem prove
    thales_1 We want to prove the sentense: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  13. Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  14. Basket of fruit
    hrusky_jablka In six baskets, the seller has fruit. In individual baskets, there are only apples or just pears with the following number of fruits: 5,6,12,14,23 and 29. "If I sell this basket," the salesman thinks, "then I will have just as many apples as a pear." Which
  15. Legs
    zidle In the room are four-legged chairs, three-legged stool, and all are sitted with (one) people. I counted all the leg room and there were a total of 39. How many are there chairs, stool and people?
  16. Gauss
    kfgauss Help little C.F. Gauss sum all the integers from 1 to 400.
  17. Find two
    eq222_7 Find two consecutive natural numbers whose product is 1 larger than their sum. Searched numbers expressed by a fraction whose numerator is the difference between these numbers and the denominator is their sum.