Question

A wizard walks into a wand shop to

purchase a magic wand. He chooses
a wand that is 22 cm long. Will the
wand fit into the box shown? Explain.

Answer 1

No. You can see this because the length of the box is 21, whilst the length of the wand is 22.

Answer 2

Yes, it can fit in.

Using Pythagoras theorem:

Find bottom side, hypotenuse

a² + b² = c²

6² + 21² = (bottom side)²

bottom side = √477

bottom side = 3√53 cm

Then find upper diagonal, hypotenuse

(3√53)² + 5² = diagonal²

diagonal = √502

diagonal = 22.4 cm

Thus the wand can fit in the box diagonally.