Find the perimeter of Pattern 6 in the form a + square root b where a and b are whole numbers...

Question

anonymous · Answer

attachment

anonymous · Answer

If you cannot read it correctly it says: Patterns are generated as shown in the diagram. Find the perimeter of Pattern 6 in the form a + √ b where a and b are whole numbers. Please show working.

phi · Answer

Did you try to do this?  The perimeter is length of all the sides, so for pattern 1, it is distance around the right triangle.
The two legs are each 1.  The hypotenuse we get from
a*a + b*b = c*c
Here a=1, and b=1, so c^2= 1+1 =2
and c= sqrt(2)
So the perimeter is 1+1+sqrt(2)= 2+sqrt(2)

phi · Answer

|dw:1328653940941:dw|
the second pattern is 1+1+1+sqrt(3) = 3+sqrt(3)
Do you see the pattern?