Question

What is the perimeter of the triangle with vertices $A(-4,2),B(0,-1)$ and $C(3,3)$?

• A. $7+3\sqrt{2}$
• B. $10+5\sqrt{2}$
• C. $11+6\sqrt{2}$
• D. $5+10\sqrt{2}$

Answer 1

The correct option is B $10+5\sqrt{2}$

Given : $A(-4,2),B(0,-1)$ and $C(3,3)$

Now distance between A and B $=\sqrt{(4{)}^2+(-3{)}^2}=5$

Distance between A and C $=\sqrt{(7{)}^2+(1{)}^2}=5\sqrt{2}$

Distance between B and C $=\sqrt{(3{)}^2+(4{)}^2}=5$

So perimeter $=AB+BC+AC=10+5\sqrt{2}$

Hence, option B is correct.