SOLUTION: We want to place the largest rod we can in a box. To figure this out we will need to do the Pythagorean Theorem two times. If the box is 4 x 3 x 2, find the longest rod that wo

Question 1067982: We want to place the largest rod we can in a box. To figure this out we will need to do
the Pythagorean Theorem two times. If the box is 4 x 3 x 2, find the longest rod that would fit in the box.

Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let the length of the box be 4 units long.
let the width of the box be 3 units long.
leg the height of the box be 2 units long.

find the diagonal of the length and the width.
that's your first right triangle.
the length is 4 and the width is 3.
the hypotenuse of the right triangle is the diagonal.
sqrt(4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5
that's the length of the diagonal of the bottom base.

you now need to find the length of the diagonal using the diagonal of the base and the height as the legs.

this forms another right triangle with the legs of 5 and 2 units long.

the hypotenuse is equal to sqrt(5^2 + 2^2) = sqrt(25 + 4) = sqrt(29).

that's your longest diagonal, whose length is sqrt(29) which is approximately equal to 5.3852 units long rounded to 4 decimal places.

the following link describes the procedure.

https://sites.google.com/site/geometry4sage20112012/home/resources/star-lessons/geometric-solids-part-1

the picture you are looking for looks like this:

the first diagonal you are solving for is DB taken from right triangle DAB.

the second diagonal you are solving for is HB taken from right triangle HDB.

HB is the longest diagonal you will find in the geometric solid.

in the diagram shown:

AB = 3
AD = 4
DB = 5
HD = 2
HB = sqrt(29)
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

We want to place the largest rod we can in a box. To figure this out we will need to do
the Pythagorean Theorem two times. If the box is 4 x 3 x 2, find the longest rod that would fit in the box.

The longest rod represents the HYPOTENUSE of the triangle formed by the DIAGONAL of the base of the box and the height of the box.
Let's name that diagonal AB
We then get:
AB, or length of longest rod =
RELATED QUESTIONS
We can use the Pythagorean theorem to solve problems that involve right triangles.... (answered by Alan3354)
how, in simple terms, can we prove the Pythagorean... (answered by nerdybill)
I was given a project to take a rectangular prism (like a cereal box)and get all the... (answered by ankor@dixie-net.com)
We need to figure out the surface area of a room so we can figure out how much paint to... (answered by Fombitz)
http://prntscr.com/a8z5eq So, I figured out 24 meters for a using the altitude is the... (answered by rothauserc)
I place 20 pounds in a box. So do you. Now the box contains 40 pounds, and we both... (answered by Alan3354)
We have a random variable with a standard deviation 10. If we want the spread in sample... (answered by jim_thompson5910)
We have a 40% solution and we want 75 liters of a 15% acid solution. How much water... (answered by josgarithmetic)
Hello! I am having trouble with my algebra homework. On one of the equasions we need to... (answered by stanbon)