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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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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
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)

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

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