Question

A square root of paper 150 millimeters on a side is folded in half along a diagonal. The result is a 45° -45° -90° triangle. What is the length of the hypotenuse of this triangle in millimeters? Write your answer in simplified radical form, if necessary.

Answer 1

The length of the hypotenuse of this triangle is 150√2 mm.

Explanation:

Consider the square ABCD shown in the image below.

The sides are 150 mm each.

All the angles of a square are 90°.

Now The square is folded in half along the diagonal BD.

The angles A, B and D are: 45°, 45° and 90°.

The hypotenuse of the right angled triangle is BD.

Compute the length of BD using the pythagoras theorem as follows:

`BD^(2)=AB^(2)+AD^(2)\\=150^(2)+150^(2)\\=2* 150^(2)\\BD=\sqrt{2* 150^(2)}\\=150√(2)`

Thus, the length of the hypotenuse of this triangle is 150√2 mm.