Answer:
Perimeter of rectangle = 6√26 or 30.59 units
Step-by-step explanation:
Let the rectangle ABCD
so, co-ordinate of A= (-6,4) = (x1,y1)
co-ordinate of B= (4,2) = (x2,y2)
co-ordinate of C= (3,-3) = (x3,y3)
co-ordinate of D= (-7,-1) = (x4,y4)
In rectangle ABCD
AB = CD ( opposite sides of rectangle are equal)
and, AD = BC ( opposite sides of rectangle are equal)
Now, using distance formula
AB = √(x2-x1)² + (y2-y1)²
=√(4-(-6))²+ (2-4)²
=√(4+6)² + (-2)²
=√(10)² + (4)
=√100+4
=√104
=2√26 units
so,AB = CD = 2√26 units
again,by using distance formula
BC = √(x3-x2)² + (y3-y2)²
=√(3-4)² + ( -3-2)²
=√(-1)² + (-5)²
=√1 + 25
=√26 units
so, AD = BC =√26 units
Now,
Perimeter of rectangle = 2(length of rectangle+breadth of rectangle)
=2(2√26 + √26) (AB =CD = 2√26 units & AD = BC = √26 units)
=2.3√26
=6√26 units
Answer is 6√26 or 30.59 units
