SOLUTION: 5 similar rectangles are used to form a big rectangle. If the area of the big rectangle is 240 square centimetres, what is its perimeter?

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Question 724841: 5 similar rectangles are used to form a big rectangle.
If the area of the big rectangle is 240 square centimetres, what is its perimeter?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
It is not clear to me how the 5 rectangles would be arranged.
If 5 congruent rectangles were attached to one another by their long sides to form a similar, larger rectangle, it would look like this:
with a and b being the small rectangles' sides' measures in cm.
Since the large rectangle is similar to the small ones,
5a%2Fb=b%2Fa --> 5a%5E2=b%5E2 --> sqrt%285%29%2Aa=b

So the area of the large rectangle is
%285a%29%2Ab=240 --> %285a%29%2A%28sqrt%285%29%2Aa%29=240 --> 5a%5E2%2Asqrt%285%29=240
Multiplying both sides of the equal sign times sqrt%285%29 we get
5a%5E2%2Asqrt%285%29%2Asqrt%285%29=240%2Asqrt%285%29 --> 25a%5E2=240%2Asqrt%285%29 --> a%5E2=240%2Asqrt%285%29%2F25 --> a=sqrt%28240%29%2Asqrt%28sqrt%285%29%29%2Fsqrt%2825%29 --> a=sqrt%2816%2A15%29%2Aroot%284%2C5%29%2F5 --> a=sqrt%2816%29%2Asqrt%2815%29%2Aroot%284%2C5%29%2F5 --> a=4sqrt%2815%29%2Aroot%284%2C5%29%2F5
Then,
b=sqrt%285%29%2A4sqrt%2815%29%2Aroot%284%2C5%29%2F5 --> b=4sqrt%285%2A15%29%2Aroot%284%2C5%29%2F5 --> b=4sqrt%2825%2A3%29%2Aroot%284%2C5%29%2F5 --> b=4sqrt%2825%29%2Asqrt%283%29%2Aroot%284%2C5%29%2F5 --> b=4%2A5%2Asqrt%283%29%2Aroot%284%2C5%29%2F5 --> b=4sqrt%283%29%2Aroot%284%2C5%29
and 5a=4sqrt%2815%29%2Aroot%284%2C5%29

The perimeter would be
2%28length%2Bwidth%29=2%285a%2Bb%29
That is