Question

Find the perimeter and area of the given triangle:

Answer 1

The perimeter is 13.213 units.

The area is 7 square units

Explanation:

O=(0,0)=(xo,yo)→xo=0, yo=0

A=(5,2)=(xa,ya)→xa=5, ya=2

B=(3,4)=(xb,yb)→xb=3, yb=4

Perimeter: P=OA+AB+OB

`OA=\sqrt{(xa-xo)^(2)+(ya-yo)^(2)}\\ OA=\sqrt{(5-0)^(2)+(2-0)^(2)}\\ OA=\sqrt{(5)^(2)+(2)^(2)}\\ OA=√(25+4)\\ OA=√(29)`

`AB=\sqrt{(xb-xa)^(2)+(yb-ya)^(2)}\\ AB=\sqrt{(3-5)^(2)+(4-2)^(2)}\\ AB=\sqrt{(-2)^(2)+(2)^(2)}\\ AB=√(4+4)\\ AB=√(8)\\ AB=√(4*2)\\ AB=√(4)√(2)\\ AB=2√(2)`

`OB=\sqrt{(xb-xo)^(2)+(yb-yo)^(2)}\\ OB=\sqrt{(3-0)^(2)+(4-0)^(2)}\\ OB=\sqrt{(3)^(2)+(4)^(2)}\\ OB=√(9+16)\\ OB=√(25)\\ OB=5`

P=OA+AB+OB

P=√29+2√2+5

P=5.385+2(1.414)+5

P=5.385+2.828+5

P=13.213

Area: A

`A=(x_(o) y_(a)+x_(a) y_(b)+x_(b) y_(o)-(y_(o) x_(a)+y_(a) x_(b)+y_(b) x_(o)) )/(2)`

`A=((0)(2)+(5)(4)+(3)(0)-[(0)(5)+(2)(3)+(4)(0)] )/(2)`

`A=(0+20+0-(0+6+0))/(2)\\ A=(20-(6))/(2)\\ A=(20-6)/(2)\\ A=(14)/(2)\\ A=7`