Chapter 6.4, Problem 37STP

To determine

To find: Percentage of increase in area.

Answer to Problem 37STP

So, the Percent of increase in area is $800\%$ .

Explanation of Solution

Given information:

Length of rectangle $=10$ inches.

Width of rectangle $=8$ inches.

Percent of change $=\frac{A}{O}\times 100$

Where

  $A=$ Amount of change.

  $O=$ Original amount.

From given information

Length of rectangle $=10$ inches.

Width of rectangle $=8$ inches.

Area of rectangle = length $\times$ width

Therefore

Area of original rectangle $=10\times 8$

  $\Rightarrow$ Area of rectangle $=80$

Given

Each dimension of rectangle is tripled.

Therefore,

Length of new rectangle $=3\times 10=30$ inches.

Width of new rectangle $=3\times 8=24$ inches.

Area of new rectangle $=30\times 24$

  $\Rightarrow$ Area of new rectangle $=720$

Amount of change = Area of new rectangle $-$ Area of original rectangle

  $\begin{array}{l}\Rightarrow A=720-80\\ \Rightarrow A=640\end{array}$

Therefore,

Percent of change $=\frac{640}{80}\times 100$

  $\Rightarrow$ Percent of change $=\frac{64000}{80}$

  $\Rightarrow$ Percent of change $=800$

So, the Percent of increase in area is $800\%$ .