Question 1045516
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ABCD is a rectangle such that AD = 2AB and the diagonal AC = root5 d the the perimeter of rectangle ABCD=?
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We know AB=CD.

AC=BD={{{sqrt(5)}}}.

Perimeter={{{2AD+2AB}}}.

Let {{{AB}}}={{{x}}}.  Then {{{AD}}}={{{2x}}}.

You have right angle triangle

{{{x^2}}} + {{{(2x)^2}}} = {{{(sqrt(5))^2}}},

{{{5x^2}}}={{{5}}},

x = 1.

Then AB = 1, AD = 2, and the perimeter = 1 + 2 + 1 + 2 = 6 units.

<U>Answer</U>.  The perimeter is 6 units.
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