SOLUTION: Find the area of the rectangle top side of the rectangle is sqrt (3) + sqrt (5) side of the rectangle is sqrt (3) + sqrt (5)

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Question 99152: Find the area of the rectangle
top side of the rectangle is sqrt (3) + sqrt (5)
side of the rectangle is sqrt (3) + sqrt (5)
Answer by Adam(64) About Me  (Show Source):
You can put this solution on YOUR website!
It is the special case of rectangle where all sides have same length, which we denote a. There is formula for surface area of rectangle with side a S+=+a%5E2 Thus S+=+%28sqrt%283%29%2Bsqrt%285%29%29%5E2
we can use %28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2
3+2*(sqrt(3)*sqrt(5)+5
now we can use sqrt%28x%29+=+x%5E%281%2F2%29 and a%5Ex%2Ab%5Ex=%28a%2Ab%29%5Ex and we get
=8%2B%283%2A5%29%5E1%2F2
=8%2B15%5E1%2F2
=8%2Bsqrt%2815%29 which is around 11.873
If you are interested in higher mathematics, area of rectangle can also be computed using definite integral int%28a%2Cdx%2Ca%2Cb%29 where a is constant function and integration bounds define left and right side, in our case it would be int%28sqrt%283%29%2Bsqrt%285%29%2Cdx%2C0%2Csqrt%283%29%2Bsqrt%285%29%29 = F(b)-F(a) =%28sqrt%283%29%2Bsqrt%285%29%29%2A%28sqrt%283%29%2Bsqrt%285%29%29-0 whic leads to same result.