Question 1047591
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The area of a rectangle is 30 and its diagonal is sqrt(61)  Find its dimensions and perimeter. 
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<U>Answer</U>. The rectangle is 6x5 and its perimeter is 6 + 5 + 6 + 5 = 22 units.


<pre>
xy = 30,             (1)
{{{x^2 + y^2}}} = 61.        (2)

Multiply eq.(1) by 2 and then add to eq.(2) (both sides). You will get

{{{x^2 + 2xy + y^2}}} = 61 + 60,  or

{{{(x+y)^2}}} = 121.

Then x + y = {{{sqrt(121)}}} = 11.

Express x = 11-y from the last equation. Then substitute this expression into (1). You will get

(11-y)*y = 30,  or

{{{-y^2 + 11y}}} = 30,  or

{{{y^2 - 11y + 30}}} = 0.

Factor left side:

(y-5)*(y-6) = 0.

The roots are y = 5  and/or  y = 6.
</pre>

Solved.