Chapter 4.7, Problem 58HP

To determine

To establish the relationship between the area of a square and the length of its sides.

Answer to Problem 58HP

The area of the square depends on the side of the square.

Explanation of Solution

Given information: Area of the square

Concept Used: Area of square = ${(side)}^2$

The area of square depends upon the length of its sides.

If the length of the square is smaller than one, then its area is much smaller than that.

For example,

If $side=\frac{1}{2}\text{units}$

1. , a rational number.

The Area of square = ${\left(\frac{1}{2}\right)}^2=\frac{1}{4}\text{sq}\text{.}\text{units}$

If $side=\sqrt{2}\text{units}$

1. , a irrational number.

The Area of square = ${\left(\sqrt{2}\right)}^2=2\text{sq}\text{.}\text{units}$

Hence, the area of the square depends on the side of the square.