Using the Pythagorean Theorem in Cuboids: Determining the size of the diagonal using Pythagoras' theorem

Shown below is the rectangular prism $ABCDA^1B^1C^1D^1$.

Calculate the diagonal of the rectangular prism.

$\sqrt{165}$

Look at the orthohedron below.

$D^1C^1=10$

$AA^1=12$

Calculate $A^1B$.

$2\sqrt{61}$

$ABCDA^1B^1C^1D^1$ is a rectangular prism.

$AB=7$
$AA^1=5$

Calculate the diagonal of the rectangular prism.

Not enough data

Look at the orthohedron in the figure and calculate the length of the dotted line.

$\sqrt{65}$

Look at the orthohedron in the figure below.

$DCC^1D^1$ is a square.

How long is the dotted line?

$13$

Look at the box in the drawing and calculate the indicated diagonal.

$\sqrt{113}$

Calculate the length of the dotted diagonal in the rectangular prism.

$x\sqrt{10}$

Calculate the lengths of all possible diagonals on the faces of the rectangular prism below:

$\sqrt{74},\sqrt{41},\sqrt{65}$

Look at the rectangular prism in the figure and express the length of the diagonal using the sides $EA,CD,FG$.

$\sqrt{CD^2+FG^2+EA^2}$

Look at the orthohedron below.

$DC=DD_1$

What is the length of the orthohedron's diagonal?

$\sqrt{264}$

The box $ABCDA^1B^1C^1D^1$ is shown below.

$A^1B^1=14$

$CC^1=8$

$A^1D^1=9$

Calculate the diagonal of the box.

$\sqrt{341}$

A cube has a side length of 5 cm.

Calculate the diagonal of the cube.

$5\sqrt{3}$

Look at the rectangular prism in the figure and express the length of its diagonal terms of a and b.

$\sqrt{a^2+5b^2}$

Look at the orthohedron in the figure and calculate $B^1D$.

$\sqrt{49a^2+25b^2+9}$

A rectangular prism has a height twice as long as its length.

Its width is 3 times greater than its height.

How many times greater is its diagonal than its length?

$\sqrt{41}$