Question

In the given figure, ABC is a right-angled triangle, right angle is at B. Find lengths AB and BC and hence AC.

• A. 4 unit
• B. $4\sqrt{2}$ unit
• C. $3\sqrt{2}$ unit
• D. 8 unit

Answer 1

The correct option is B

$4\sqrt{2}$ unit

Given: ABC is a right-angled triangle.

So, $A{C}^2=A{B}^2+B{C}^2$ ...(1) [By Pythagoras theorem]

$A{B}^2=(2-2{)}^2+(6-2{)}^2$ (by distance formula)
$A{B}^2=0+4=16$
$AB=4$
$B{C}^2=(6-2{)}^2+(2-2{)}^2$ (by distance formula)
$B{C}^2=4^2+0=16$
Now, putting value of AB and BC in equation (1)
$A{C}^2=A{B}^2+B{C}^2$
$\Rightarrow A{C}^2=16+16$
$\Rightarrow AC=4\sqrt{2}$