Chapter 7.3, Problem 62E

To determine

To calculate: If the area of square B is $65\%$ of the area of square A..

Answer to Problem 62E

The area of square B is not $65\%$ of area of square A.

Explanation of Solution

Given information:

Area of square A= $400$ square centimeters.

Side length of square B= $65\%$ of the side length of square A.

Calculation:

To find if the area of square B is $65\%$ of the area of square A, first find the side length of square A.

  $\begin{array}{l}\text{ Area of square A}=400\text{ square centimeters [Given]}\\ \Rightarrow \text{Side }\times \text{ side}=400\text{ square centimeters [Substitute the formula of area]}\\ \Rightarrow {\text{side}}^2=400\text{ square centimeters [Multiply]}\\ $ \Rightarrow {\text{side}}^2={(20)}^2\text{ square centimeters [Express as powers of }2]$\Rightarrow \text{side}=20\text{ centimeters}\end{array}$

Now, side of square B is $65\%$ of side of square A. Side of square B will be calculated as follows:

  $\begin{array}{l}\text{Side}=65\%\text{ of }20\text{ centimeters [Original expression]}\\ \Rightarrow \text{side }=0.65\text{ of }20\text{ centimeters [Write percent as decimal]}\\ \Rightarrow \text{side }=13\text{ centimeters [Multiply]}\end{array}$

Calculate area of square B:

  $\begin{array}{l}\text{Area of square B}=\text{side}\times \text{side [Formula]}\\ =(13\times 13)\text{ square centimeters [Substitute value of side]}\\ =169\text{ square centimeters [Multiply]}\end{array}$

Now calculate the area of square B as a percent of area of square A

  $\begin{array}{l}\frac{169}{4\cancel{0}\cancel{0}}\times 1\cancel{0}\cancel{0}\text{ [Divide out common factors]}\\ =\frac{169}{4}\text{\% [Simplify]}\\ =42.25\%\text{ [Write fraction as decimal]}\end{array}$

Therefore, the area of square B is not $65\%$ of area of square A.