Question

A box in the shape of a rectangular prism has the dimensions shown. What is the length of the interior diagonal of the box? Round to the nearest tent

Enter your answer in the box.

Answer 1

141.4 cm

Explanation:

Refer to the notations in the attached photo,

AG = d

Using Pythagoras Theorem:

In triangle ABC,

AC

=
`\sqrt{ {60}^(2) + {80}^(2) }`

=
`√(3600 + 6400)`

=
`√(10000)`

= 100 cm

∴ AC is 100 cm.

In triangle ACG,

d

=
`\sqrt{ {100}^(2) + {100}^(2) }`

=
`√(10000 + 10000)`

=
`√(20000)`

= 141.4 cm (cor. to the nearest tenth)