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

Answer:

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

Step-by-step 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:

$BD^{2}=AB^{2}+AD^{2}\\=150^{2}+150^{2}\\=2\times 150^{2}\\BD=\sqrt{2\times 150^{2}}\\=150\sqrt{2}$

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