# 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:

$a+b=10 \ \\ c+d = 5 \ \\ x^2 = b^2 +c^2 \ \\ 1^2 = a^2 +d^2 \ \\ \ \\ y = x^2 = (10-a)^2 + (5-\sqrt{ 1-a^2})^2 \ \\ y = x^2 = -10 \sqrt{ 1-a^2} - 20 a + 126 \ \\ \ \\ y' = \dfrac{ 10 a}{ \sqrt(1-a^2)} -20 \ \\ y' = 0 \ \\ a = \dfrac{2}{\sqrt{5}} = 0.894427191 \ m \ \\ x = \sqrt{y} = \sqrt{ -10 \sqrt(1-a^2)-20 a+126 } \ \\ x = 10.18034 \ \text{m}$

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

Tips to related online calculators
Do you want to convert length units?
Pythagorean theorem is the base for the right 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:

## Next similar math problems:

• Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
• Rectangular field
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.
• Top of the tower
The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m, the pyramid height is 1.6 m. How many square meters of sheet metal is needed to cover the top of the tower if 15% extra sheet metal is needed for joint
• Rectangle diagonals
It is given rectangle with area 24 cm2 a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
• Diagonal 20
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?
• Rectangular garden
The sides of the rectangular garden are in ratio 1: 2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden.
• A cylinder
A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the cylinder's top and bottom. (forming a spiral around the cylinder). How long is the string in cm?
• Rectangular trapezoid
The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate trapezium area in cm square and calculate how many differs perimeters of the
• The tent
The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m2 of cloth we need to make the tent if we have to add 7% of the seams? How many m3 of air will be in the tent?
• Chocolate roll
The cube of 5 cm chocolate roll weighs 30 g. How many calories will contain the same chocolate roller of a prism shape with a length of 0.5 m whose cross section is an isosceles trapezoid with bases 25 and 13 cm and legs 10 cm. You know that 100 g of this
• Cuboid face diagonals
The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid.
• A rectangle 2
A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.
• Free space in the garden
The grandfather's free space in the garden was in the shape of a rectangular triangle with 5 meters and 12 meters in length. He decided to divide it into two parts and the height of the hypotenuse. For the smaller part creates a rock garden, for the large
• Integer sides
A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side?
• ABCD square
In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment?
• The garden
The garden has the shape of a rectangular trapezium. The bases have lengths of 27 meters and 36 meters, the trapezoid's height is 12 meters. Calculate how much fence will cost this garden if one meter costs 1.5 €?
• Triangular prism
The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism.