SOLUTION: a rectangle has length 2squarerootxcm and width squarerootxcm. the length of a diagonal of the rectangle is the squareroot of 45cm. 1 find the area of the rectangle 2 the area of

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Question 739994: a rectangle has length 2squarerootxcm and width squarerootxcm. the length of a diagonal of the rectangle is the squareroot of 45cm.
1 find the area of the rectangle
2 the area of the square is twice the area of the rectangle.
find the length of a side of a square.
Found 2 solutions by lynnlo, ikleyn:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by ikleyn(53431) About Me  (Show Source):
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a rectangle has length 2squarerootxcm and width squarerootxcm. the length of a diagonal of the rectangle is the squareroot of 45cm.
1 find the area of the rectangle
2 the area of the square is twice the area of the rectangle.
find the length of a side of a square.
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             P a r t   1.


The length is  2sqrt%28x%29.  The width is  sqrt%28x%29.

The diagonal is  sqrt%28%282sqrt%28x%29%29%5E2+%2B+%28sqrt%28x%29%29%5E2%29 = sqrt%284x+%2B+x%29 = sqrt%285x%29.


From the problem, we have this equation

    sqrt%285x%29 = sqrt%2845%29.


Square both sides

    5x = 45

and find  x = 45/5 = 9.


Then the area of this rectangle is  Length*Width = %282sqrt%289%29%29%2Asqrt%289%29 = 2*9 = 18 cm^2.   ANSWER


Part 1 is complete.



             P a r t   2.


The area of the square is twice the area of the rectangle, i.e.  2*18 = 36 cm^2.


Hence, the side of the square is  sqrt%2836%29 = 6 cm.    ANSWER


Part 2 is complete.

The problem is fully solved.