Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

An envelope measures $9$ centimeters by $40$ centimeters. A pencil is placed in the envelope at a diagonal. What is the maximum possible length of the pencil? $\newline$ _____ centimeters

View step-by-step help

View step-by-step help

Pythagorean theorem

Full solution

Q. An envelope measures

9

centimeters by

40

centimeters. A pencil is placed in the envelope at a diagonal. What is the maximum possible length of the pencil?

\newline

_____ centimeters

Form Right Triangle: The envelope and the pencil form a right triangle, with the envelope's length and width as the legs, and the pencil as the hypotenuse.
Use Pythagorean Theorem: Using the Pythagorean Theorem: $a^2 + b^2 = c^2$ , where $a$ and $b$ are the legs, and $c$ is the hypotenuse.
Plug in Dimensions: Plug in the envelope's dimensions for $a$ and $b$ : $9^2 + 40^2 = c^2$ .
Calculate Squares: Calculate the squares: $81 + 1600 = c^2$ .
Add Squares: Add the squares: $81 + 1600 = 1681$ .
Solve for Hypotenize: Solve for $c$ by taking the square root of $1681$ : $c = \sqrt{1681}$ .
Calculate Square Root: Calculate the square root: $c = \sqrt{41}$ .

More problems from Pythagorean theorem

Question

A multi-layer cake is in the shape of a right cylinder. The height of the cake is

20

(\mathrm{cm})

, and its radius is

10 \mathrm{~cm}

. If each of the cake layers has a volume of approximately

1

250

cubic centimeters, then how many layers does the cake have?

Posted 6 months ago

Question

A right pyramid with a square base has a volume of

252

cubic centimeters. The length of one of the sides of its base is

6

centimeters. Rounded to the nearest centimeter, what is the vertical height of the pyramid?

Posted 10 months ago

Question

\mathrm{Ji}

-Hun and Kana are running a marathon. Due to the volume of people running, the starts occur in waves. Kana starts at

9: 35

\mathrm{a} . \mathrm{m}

. and runs at an average rate of

7

miles per hour (mph). Ji-Hun starts at

10: 00

\mathrm{a} . \mathrm{m}

. and runs at an average rate of

8 \mathrm{mph}

. Assuming constant paces and no stops, to the nearest tenth of a mile, in how many miles will Ji-Hun catch up to Kana?

Posted 6 months ago

Question

Imani's grandmother's house is

5

miles west of her own house down Main Street. While at her grandmother's, Imani decides to ride her bike farther west down Main Street at

10

miles per hour. Which equation best describes the distance,

d

, in miles, Imani is from home after

t

\newline

1

\newline

d=5+10 t

\newline

d=5-10 t

\newline

d=5 t+10

\newline

d=5 t-10

Posted 10 months ago

Question

Mr. Mole left his burrow and started digging his way down.

\newline

A

represents Mr. Mole's altitude relative to the ground (in meters) after

t

\newline

A=-2.3 t-7

\newline

How far below the ground does Mr. Mole's burrow lie?

\newline

meters below the ground

Posted 10 months ago

Question

To get to school, Da'Quon walks

0

6

miles from his house to the bus stop. He then takes the bus for

3

9

miles. After he gets off the bus, he can choose one of several walking routes to school. The total number of miles he travels, via walking and bus, does not exceed

5

4

. What is the greatest possible number of miles he walks after getting off the bus?

\newline

1

\newline

0

0

\newline

0

3

\newline

0

9

\newline

1

5

Posted 10 months ago

Question

The chambered nautilus is a deepsea creature with a spiral shell that can withstand pressure up to

1180

pounds per square inch (psi). Underwater pressure consists of atmospheric pressure, which is

14.7 \mathrm{psi}

0.45 \mathrm{psi}

of hydrostatic pressure per foot of depth under water. To the nearest foot, what is the maximum depth under water at which the shell of a chambered nautilus can withstand the pressure?

Posted 10 months ago

Question

A rectangular prism and cube have equal volumes. The length of the rectangular prism is

12

(\mathrm{cm})

and its width is

8 \mathrm{~cm}

. If each side of the cube is

12 \mathrm{~cm}

, then what is the height of the rectangular prism in centimeters?

Posted 7 months ago

Question

Emeka forms a ball of clay with a radius of

3

(\mathrm{cm})

. He then reforms the clay into a cylinder of radius

2 \mathrm{~cm}

. What is the height of the cylinder in centimeters, rounded to the nearest tenth?

Posted 7 months ago

Question

A cube of gold with an edge length of

3

inches (in) is melted and reformed into a rectangular prism with a width of

2

5

in and a height of

2 \mathrm{in}

. If the volume is unchanged during melting, what is the length of the prism of gold in inches?

Posted 1 year ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant