Chapter 6.2, Problem 29WE

To determine

To calculate: The area of the square with side length $\frac{2x}{7}\text{ in}$.

Answer to Problem 29WE

The area of the square is $\frac{4x^2}{49}\text{ in}$.

Explanation of Solution

Given information:

A square with side length of $\frac{2x}{7}\text{ in}$.

Formula used:

Area $\left(A\right)$ of square is square of its side. Let side of the square be of length $\left(l\right)$ . It is mathematically denoted by $A=l^2$.

Law of exponent for a quotient raised to power m where m is a positive integer is ${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$.

Law of exponent for a product of two terms raised to power m where m is a positive integer is ${\left(ab\right)}^m=a^m{b}^m$.

Calculation:

Consider the provided statement a square with side length $\frac{2x}{7}\text{ in}$.

Recall that area $\left(A\right)$ of square is square of its side. Let side of the square be of length $\left(l\right)$ . It is mathematically denoted by $A=l^2$ .Recall that law of exponent for a quotient raised to power m where m is a positive integer is ${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$ and law of exponent for a product of two terms raised to power m where m is a positive integer is ${\left(ab\right)}^m=a^m{b}^m$.

Apply it,

  $\begin{array}{c}A=l^2\\ ={\left(\frac{2x}{7}\text{ in}\right)}^2\\ =\frac{{\left(2x\right)}^2}{7^2}{\text{ in}}^{\text{2}}\\ =\frac{4x^2}{49}{\text{in}}^{\text{2}}\end{array}$

Thus, the area of the square is $\frac{4x^2}{49}\text{ in}$.