Chapter 12, Problem 7CUR

To determine

To check: Whether the given statement is true or false.

Answer to Problem 7CUR

The given statement is False.

Explanation of Solution

Given information: The statement is “The area of a triangle with sides $3$ , $3$ , and $2$ is $4\sqrt{2}$ ”.

It can be observed that the two sides of the triangle are equal. So, it is an isosceles triangle.

Consider $2$ as the base and divide it into half to find the altitude of the triangle. Now, use Pythagoras Theorem to find the length of altitude as:

  $\begin{array}{c}{H}^2=P^2+B^2\\ 3^2=P^2+1^2\\ P^2=9-1\\ P=2\sqrt{2}\end{array}$

So, the altitude of the given triangle is $2\sqrt{2}$ .

  

The formula for area of triangle is:

  $A=\frac{1}{2}bh$

Substitute $2$ for $b$ and $2\sqrt{2}$ for $h$ in the formula.

  $\begin{array}{c}A=\frac{1}{2}\cdot 2\cdot 2\sqrt{2}\\ =2\sqrt{2}\end{array}$

So, the area of the given triangle is $2\sqrt{2}$ not $4\sqrt{2}$ .

Therefore, the given statement is false.