Using the Pythagorean Theorem in Cuboids: Using Pythagoras' theorem to calculate the height of a box

Look at the orthohedron in the figure.

$A^1B=12$

Canculate $CC^1$.

$2\sqrt{11}$

Look at the rectangular prism below.

$ABCDA^1B^1C^1D^1$

$BC^1=12$

$D^1D=10$

$D^1C=7$

Calculate AD.

$2\sqrt{11}$ cm

Look at the rectangular prism in the figure below.

Calculate AD.

$2\sqrt{22}$ cm

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


$D^1C^1=14$

$BD=20$

Calculate the height of the rectangular prism.

$2\sqrt{51}$ cm

Look at the rectangular prism in the figure below.

The length of the diagonal is $2\sqrt{14}$ cm.

Calculate $BB^1$.

$2$

A rectangular prism has a diagonal length of $2\sqrt{30}$ cm.

It is $4$ cm high and $2$ cm wide.

Calculate the length of the rectangular prism.

$10$ cm

Look at the rectangular prism in the figure below and calculate $CC^1$.

$\sqrt{139}$ cm

Look at the rectangular prism in the figure below.

Calculate the length of $DD^1$.

$6\sqrt{2}$ cm

$ABCDA^1B^1C^1D^1$ is an orthohedron.

$BC^1=2x$

$A^1D^1=3y$

Express $BB^1$ in terms of x and y.

$\sqrt{4x^2-9y^2}$

Look at the orthohedron in the figure below.

$BC^1=2AA^1$
$A^1D^1=5$

Calculate $AA^1$.

$\frac{5}{\sqrt{3}}$ cm

Look at the rectangular prism below and calculate $BC$.

$2\sqrt{145}$

Look at the orthohedron in the figure below.

Calculate $DE$.

It is not possible to calculate.

A rectangular prism has a diagonal length of 24 cm.

The surface area of one of the faces is 40 cm² and its side measures 4 cm.

Calculate the dimensions of the rectangular prism.

$10,4,2\sqrt{115}$

Look at the orthohedron below.

$B^1C^1=7x$

$DC=4x$

$BD^1=2\sqrt{26}x$

Calculate $AA^1$.

$x\sqrt{39}$

Look at the rectangular prism in the figure below.

The diagonal is $13x$ long.

$A^1D^1=2y$

$A^1B^1=2x$

Calculate $DD^1$.

$\sqrt{165x^2-4y^2}$