Question 1192198
A rectangle has sides of length (2+ √18)metre and (5-4/√2)metres.
If you mean {{{5 - 4/sqrt(2)}}}:
{{{5 - 4/sqrt(2) = 5 - 2sqrt(2)}}}
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.
{{{Area = (2 + 3sqrt(2))*(5 - 2sqrt(2)) = 10 + 11sqrt(2) - 12 = -2 + 11sqrt(2)}}}
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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 = {{{(2+ 3sqrt(2))^2 + (5-2sqrt(2))^2}}}
{{{D^2 = (4 + 12sqrt(2) + 18) + (25 -20sqrt(2) + 8)}}}
{{{D^2 = 55 - 8sqrt(2)}}}