Question

A rectangular box of height 10 has a base with edges of length 10. What is the length of a diagonal of this box?

Answer 1

Answer:

The diagonal of the box is $D=10\sqrt{3}\ units$

Step-by-step explanation:

Let

d ----> the diagonal of the base

D ---> the diagonal of the box

step 1

Find the diagonal of the base

Applying the Pythagorean Theorem

$d^2=10^2+10^2$

$d^2=200$

$d=10\sqrt{2}\ units$

step 2

Find the diagonal of the box

In this part the legs of the right triangle are the height of the box and the diagonal of the base

so

Applying the Pythagorean Theorem

$D^2=10^2+(10\sqrt2)^2$

$D^2=300$

$D=10\sqrt{3}\ units$