Question

A diagram shows a 5 cm* 5 cm* 5 cm cube.Calculate the length of the diagonal AB. Give your answer correct to 1 decimal place

Answer 1

The length of the diagonal AB of the given square is 8.660

Given that a diagram of a cube having dimensions 5×5×5 and asked to find out the length of diagonal AB(which is a body diagonal of the cube).

To calculate the body diagonal 1st we need to calculate the face diagonal via the Pythagorean theorem

Let's assume the length of the face diagonal is x

By Pythagorean theorem

$x^{2} =5^{2} + 5^{2}$

$x^{2} =50$

$x=5\sqrt{2}$

Therefore, the length of the face diagonal is $5\sqrt{2}$

Let's assume the body diagonal is y

By Pythagorean theorem

$y^{2} =5^{2} +(5\sqrt{2} )^{2}$

$y=\sqrt{125}$

y=$5\sqrt{3}$=8.660

Therefore, The length of the diagonal AB of the given square is 8.660

Learn more about diagonal here:

brainly.com/question/12274248                              

#SPJ9