Question

The bulletin board is in the shape of a square. Find two rational numbers that are within 1/8 inch of the actual side lenghth.Area= 150 square units

Answer 1

The given area of the square is:

$A=150\text{ units\textasciicircum2}$

The area of a square is given by the formula:

$A=s^2$

If we replace the given value we obtain:

$\begin{gathered} 150=s^2 \\ s=\sqrt{150} \end{gathered}$

The result of this square root is not an integer, and the closest square roots that are exact numbers are:

$\begin{gathered} \sqrt{144}<\sqrt{150}<\sqrt{169} \\ 12<\sqrt{150}<13 \end{gathered}$

As the rational numbers need to be within 1/8 inch of the actual side length, it is:

$x<\frac{\sqrt{150}}{8}$

As the square root of 150 is between 12 and 13, we can use any two whole numbers that are less than 13 and divide by 8 to obtain a number less than sqrt(150)/8, for example, 12:

$\begin{gathered} \frac{12}{8}<\frac{\sqrt{150}}{8} \\ \\ \text{ Simplify} \\ \frac{\frac{12}{4}}{\frac{8}{4}}=\frac{3}{2} \end{gathered}$

Now, another number could be 10, so:

$\begin{gathered} \frac{10}{8}<\frac{\sqrt{150}}{8} \\ \\ \text{ Simplify} \\ \frac{\frac{10}{2}}{\frac{8}{2}}=\frac{5}{4} \end{gathered}$

Two rational numbers that are within 1/8 inch of the actual side length could be: 3/2 and 5/4