SOLUTION: Find the area of the rectangle. Top side= square root of 3 + square root of 5 and the right side= square root of 3 + square root of 5

Algebra ->  Rectangles -> SOLUTION: Find the area of the rectangle. Top side= square root of 3 + square root of 5 and the right side= square root of 3 + square root of 5      Log On


   

Question 118066: Find the area of the rectangle. Top side= square root of 3 + square root of 5 and the right side= square root of 3 + square root of 5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember the area of a rectangle is A=L%2AW. So the area is

A=%28sqrt%283%29+%2B+sqrt%285%29%29%28sqrt%283%29+%2B+sqrt%285%29%29 Plug in L=sqrt%283%29+%2B+sqrt%285%29 and W=sqrt%283%29+%2B+sqrt%285%29



Now let's foil the expression to find the area



%28sqrt%283%29%2Bsqrt%285%29%29%28sqrt%283%29%2Bsqrt%285%29%29 Start with the given expression

Remember, when you FOIL an expression, you follow this procedure:


%28highlight%28sqrt%283%29%29%2Bsqrt%285%29%29%28highlight%28sqrt%283%29%29%2Bsqrt%285%29%29 Multiply the First terms:%28sqrt%283%29%29%2A%28sqrt%283%29%29=sqrt%283%29%5E2=3


%28highlight%28sqrt%283%29%29%2Bsqrt%285%29%29%28sqrt%283%29%2Bhighlight%28sqrt%285%29%29%29 Multiply the Outer terms:%28sqrt%283%29%29%2A%28sqrt%285%29%29=sqrt%283%29sqrt%285%29=sqrt%283%2A5%29=sqrt%2815%29


%28sqrt%283%29%2Bhighlight%28sqrt%285%29%29%29%28highlight%28sqrt%283%29%29%2Bsqrt%285%29%29 Multiply the Inner terms:%28sqrt%285%29%29%2A%28sqrt%283%29%29=sqrt%285%29sqrt%283%29=sqrt%285%2A3%29=sqrt%2815%29


%28sqrt%283%29%2Bhighlight%28sqrt%285%29%29%29%28sqrt%283%29%2Bhighlight%28sqrt%285%29%29%29 Multiply the Last terms:%28sqrt%285%29%29%2A%28sqrt%285%29%29=sqrt%285%29%5E2=5


3%2Bsqrt%2815%29%2Bsqrt%2815%29%2B5 Now collect every term to make a single expression



8%2B2sqrt%2815%29 Now combine like terms


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Answer:
So %28sqrt%283%29+%2B+sqrt%285%29%29%28sqrt%283%29+%2B+sqrt%285%29%29 foils and simplifies to 8%2B2sqrt%2815%29

In other words, %28sqrt%283%29+%2B+sqrt%285%29%29%28sqrt%283%29+%2B+sqrt%285%29%29=8%2B2sqrt%2815%29


So the area is A=8%2B2sqrt%2815%29