Chapter 12.5, Problem 50SR

To determine

To calculate: the area of the triangle and a simplified radical expression.

Answer to Problem 50SR

The radical expression of the area of rectangle is $4\cdot 2\sqrt{10}\times 3\sqrt{5}$

The area of the rectangle is $169.7\text{square centimeters}$

Explanation of Solution

Given information:

Width of rectangle is $3\sqrt{5}$ centimeters and length of rectangle is $4\sqrt{40}$ centimeters

Formula used:

  $areaof\text{ rectangle=}\left(length\right)\times \left(width\right)$

Calculation :

The radical expression of the area of rectangle

  $\begin{array}{l}4\sqrt{40}\times 3\sqrt{5}\\ 4\cdot 2\sqrt{10}\times 3\sqrt{5}\end{array}$

The area of the rectangle

  $\begin{array}{l}=4\cdot 2\sqrt{10}\times 3\sqrt{5}\\ =169.7\text{square centimeters}\end{array}$

Therefore,

The area of the rectangle is $169.7\text{square centimeters}$