Question

What is the length of the diagonal, d, of the cube shown.

Answer 1

`\begin{gathered} \\ d=103.9 \end{gathered}`

Step-by-step explanation

Step 1

we have a rigth triangle here, then we can use Pythagotas theorem

`side^2_1+side^2_2=hypotenuse^2`

Let

Step 2

find the sides

side1=60

for side 2

then

`\begin{gathered} side_2^2=60^2+60^2 \\ \text{side}^2_2\text{= 3600+3600} \\ \text{side}_2=\sqrt[]{7200} \end{gathered}`

Step 3

Let

`\begin{gathered} \text{side}_1=60 \\ \text{side}_2=\sqrt[]{7200} \\ \text{hypotenuse = h} \end{gathered}`

replace

`\begin{gathered} side^2_1+side^2_2=hypotenuse^2 \\ 60^2+(\sqrt[]{7200})^2=h^2 \\ 3600+7200=h^2 \\ 10800=h^2 \\ h=\sqrt[]{10800}=\text{ 103.92} \\ to\text{ the nearesth tenth } \\ 103.9 \end{gathered}`