Carpet

The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make rectangular cut of roll that piece of carpet will be longest possible and it fit into the room. How long is a piece of carpet? Note .: carpet will not be parallel with the diagonal.

Correct result:

x =  10.18034 m

Solution:

a+b=10 c+d=5 x2=b2+c2 12=a2+d2  y=x2=(10−a)2+(5−1−a2)2 y=x2=−101−a2−20a+126  y′=10a(1−a2)−20 y′=0 a=25=0.894427191 m x=y=−10(1−a2)−20a+126 x=10.18034 ma+b=10 \ \\ c+d = 5 \ \\ x^2 = b^2 +c^2 \ \\ 1^2 = a^2 +d^2 \ \\ \ \\ y = x^2 = (10-a)^2 + (5-\sqrt{ 1-a^2})^2 \ \\ y = x^2 = -10 \sqrt{ 1-a^2} - 20 a + 126 \ \\ \ \\ y' = \dfrac{ 10 a}{ \sqrt(1-a^2)} -20 \ \\ y' = 0 \ \\ a = \dfrac{2}{\sqrt{5}} = 0.894427191 \ m \ \\ x = \sqrt{y} = \sqrt{ -10 \sqrt(1-a^2)-20 a+126 } \ \\ x = 10.18034 \ \text{m}

Try another example


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!
avatar




Tips to related online calculators
Do you want to convert length units?
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

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   video2

Next similar math problems:

  • Cableway
    cable-car Cableway has a length of 1800 m. The horizontal distance between the upper and lower cable car station is 1600 m. Calculate how much meters altitude is higher upper station than the base station.
  • 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?
  • Medians and sides
    3angle Determine the size of a triangle KLM and the size of the medians in the triangle. K=(-5; -6), L=(7; -2), M=(5; 6).
  • Median
    1taznice_rt In the right triangle are sides a=41 dm b=42 dm. Calculate the length of the medians tc to the hypotenuse.
  • Triangle ABC
    lalala In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
  • Spruce height
    stromcek_7 How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree?
  • Calculate
    equilateral_triangle2 Calculate the length of a side of the equilateral triangle with an area of 50cm2.
  • RT triangle and height
    345 Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm.
  • ABS CN
    complex_num Calculate the absolute value of complex number -15-29i.
  • Euclid2
    euclid In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
  • Center of line segment
    stredna_priecka_1 Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is .
  • Vector 7
    vectors_sum0_1 Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
  • Satin
    diagonal_rectangle_3 Sanusha buys a piece of satin 2.4 m wide. The diagonal length of the fabric is 4m. What is the length of the piece of satin?
  • Isosceles triangle
    triangle2_3 The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z.
  • Billiard balls
    balls_billiard A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original.
  • Length IT
    lich2 Find the length (circumference) of an isosceles trapezoid in which the length of the bases a,c and the height h are given: a = 8 cm c = 2 cm h = 4 cm
  • Diamond
    cerveny_kosoctverec Side length of diamond is 35 cm and the length of the diagonal is 56 cm. Calculate the height and length of the second diagonal.