Chapter 12, Problem 9CUR

To determine

To check:Whether the statement “A triangle with sides of $\sqrt{3}$ , $2$ ,and $\sqrt{7}$ is a right triangle” is true or false.

Answer to Problem 9CUR

The statement “A triangle with sides of $\sqrt{3}$ , $2$ ,and $\sqrt{7}$ is a right triangle” is true.

Explanation of Solution

Given information:

The sides of the triangle are $\sqrt{3}$ , $2$ ,and $\sqrt{7}$ .

Calculation:

Let $\Delta ACB$ is a triangle. The sides are $AB=\sqrt{7}$ , $BC=\sqrt{3}$ , and $AC=2$ .

  

In a right-angled triangle, the square of $AC$ plus the square of $BC$ is equal to the square of $AB$ .

  $A{B}^2=A{C}^2+B{C}^2$

Substitute the values.

  $\begin{array}{c}AB=\sqrt{A{C}^2+B{C}^2}\\ =\sqrt{3+4}\\ =\sqrt{7}\end{array}$

From the above, it is clear that the length of the side AB is equal and it follows Pythagoras theorem.

Therefore, the statement “A triangle with sides of $\sqrt{3}$ , $2$ ,and $\sqrt{7}$ is a right triangle” is true.