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=√(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} √(144)<√(150)<√(169) \\ 12<√(150)<13 \end{gathered}`

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

`x<(√(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} (12)/(8)<(√(150))/(8) \\ \\ \text{ Simplify} \\ ((12)/(4))/((8)/(4))=(3)/(2) \end{gathered}`

Now, another number could be 10, so:

`\begin{gathered} (10)/(8)<(√(150))/(8) \\ \\ \text{ Simplify} \\ ((10)/(2))/((8)/(2))=(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