SOLUTION: A rectangle has sides of length (2+ √18)metre and (5-4/√2)metres. Express in the form a + b√2,where a and b are integers. (i) the value of A, where A square metres is the ar

Algebra ->  Test -> SOLUTION: A rectangle has sides of length (2+ √18)metre and (5-4/√2)metres. Express in the form a + b√2,where a and b are integers. (i) the value of A, where A square metres is the ar      Log On


   



Question 1192198: A rectangle has sides of length (2+ √18)metre and (5-4/√2)metres. Express in the form a + b√2,where a and b are integers.
(i) the value of A, where A square metres is the area of the rectangle.
(ii) the value of D^2, where D metres is the length of the diagonal of the rectangle.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangle has sides of length (2+ √18)metre and (5-4/√2)metres.
If you mean 5+-+4%2Fsqrt%282%29:
5+-+4%2Fsqrt%282%29+=+5+-+2sqrt%282%29
Express in the form a + b√2,where a and b are integers.
(i) the value of A, where A square metres is the area of the rectangle.

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(ii) the value of D^2, where D metres is the length of the diagonal of the rectangle.
D^2 = (2+ √18)^2 + (5-4/√2)^2 = %282%2B+3sqrt%282%29%29%5E2+%2B+%285-2sqrt%282%29%29%5E2
D%5E2+=+%284+%2B+12sqrt%282%29+%2B+18%29+%2B+%2825+-20sqrt%282%29+%2B+8%29
D%5E2+=+55+-+8sqrt%282%29