Question

What is the length of side s of the square shown below?45°6S90°A. 2.B. 6C. 3D. 5.2E. 3.2F. .6

Answer 1

The diagram shows a square with one side marked as s, while the diagonal that cuts across measures 6 units.

The diagonal results in a right angled triangle with two sides measuring 45 degrees and one side measuring 90 degrees. Now that we have a right angled with one angle, and two sides (one is given as 6, and one is unknown), we now calculate side s as follows;

`\begin{gathered} \cos 45=\frac{\text{adj}}{\text{hyp}} \\ We\text{ use the ratio for cosine because the sides shown are the} \\ \text{adjacent (between the right angle and the reference angle) and} \\ \text{hypotenuse (facing the right angle)} \\ \cos 45=(s)/(6) \\ \cos 45=\frac{1}{\sqrt[]{2}} \\ \text{Therefore,} \\ \frac{1}{\sqrt[]{2}}=(s)/(6) \\ \text{Cross multiply and you have} \\ \frac{6}{\sqrt[]{2}}=s \\ \text{Rationalize the expression and you have} \\ 3\sqrt[]{2}=s \\ \text{Therefore} \\ s=3\sqrt[]{2} \end{gathered}`

The correct answer is option E