Question

A box has dimensions 30 cm, 40 cm and 120 cm. Can you enter a stick of 128 cm inside the box?

Answer 1

The maximum length that enters in the box is 130 cm.

Yes, we can enter a stick of 128 cm in the box.

Explanation:

the maximum length that can be placed inside the box is equal to the distance between two opposite vertices of the box. In the picture attached, this distance is CF.

We start by calculating the distance CH.

We apply the Pithagorean theorem.

If CD=30 cm and DH=40 cm, CH is:

`CH^2=CD^2+DH^2=30^2+40^2=900+1600=2500\\\\CH=√(2500)=50`

Now, we apply the Pithagorean theorem again to calculate CF.

If CH=50 cm and HF=120 cm, CF is:

`CF^2=CH^2+HF^2=50^2+120^2=2500+14400=16900\\\\CH=√(16900)=130`

The maximum length that enters in the box is 130 cm.

Yes, we can enter a stick of 128 cm in the box.