Using the Pythagorean Theorem in Cuboids: Using Pythagoras' theorem- with parameters to calculate the lines of the box

Calculate the length of $BB_1$ in the box shown in the diagram.

$\sqrt{324-a^2}$

Look at the orthohedron in the figure.

$CG=\frac{1}{2}HG$

Calculate $BE$.

$x\frac{\sqrt{5}}{2}+\frac{5\sqrt{5}}{2}$

Look at the rectangular prism in the figure.

Express the length of the diagonal in terms of x, y, and z.

$\sqrt{x^2+y^2+z^2}$

Calculate the length of the dotted line in the rectangular prism below.

$\sqrt{16b^2+9a^2}$

Look at the orthohedron in the figure below.

How long is the dotted line?

$\sqrt{5b^2+8b+16}$

A rectangular prism has a diagonal length of$18ab$.

The area of one of the faces of the rectangular prism is equal to $3a^2$.

The length of the side of the face is $2b$.

Calculate the dimensions of the rectangular prism.

$\sqrt{324a^2b^2-\frac{9a^4}{4b^2}-4b^2},\\ \frac{3a^2}{2b},2b$

Look at the rectangular prism below.

Its height is $\frac{a}{2}$, its length is $3b$, and its width is $a+b$.

Calculate the diagonal of the rectangular prism.

$\sqrt{\frac{5}{4}a^2+2ab+10b^2}$

Calculate the diagonal of the rectangular prism in the figure.

It cannot be calculated.

A rectangular prism has a square base with a diagonal length of X.

The prism has a length of 3X.

How long is the diagonal of the rectangular face of the prism.

$x\sqrt{9.5}$

$ABCDEFGH$ is a rectangular prism.

$AF=\sqrt{26a^2+8a+16}$

$HG=A+4$

Calculate $AE$.

$5a$

A rectangular prism has dimensions of $5x,x+3,2x+1$.

Calculate the length of its diagonal.

$\sqrt{30x^2+10x+10}$

An orthohedron has a diagonal that is $\sqrt{5a^2+6a+b^4+9}$ long.

Its length is $2a$ and its width is $a+3$.

Calculate the dimensions of the orthohedron.

$2a,a+3,b^2$

Look at the rectangular prism below.

The length of its diagonal is:

$\sqrt{41+5n^2+9m^2+24m-20n}$

$DB=\sqrt{9m^2+n^2+24m+16}$

Calculate $CC^1$.

$2n-5$

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

The length of its diagonal is

$\sqrt{6x^2-12x+41}$.

$DC^1=\sqrt{5x^2-4x+25}$

Calculate $C^1B^1$.

$x-4$

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

$BC^1=\sqrt{5b^2+a^2-24b+8a+80+2ab}$

$AA^1=2b-8$

Calculate $A^1D$.

$a+b+4$