SOLUTION: Given a square, construct another square whose area will be 5 times the area of the original square. Make a sketch and describe the construction step by step. Hint: Use Pyth. Th

Algebra ->  Length-and-distance -> SOLUTION: Given a square, construct another square whose area will be 5 times the area of the original square. Make a sketch and describe the construction step by step. Hint: Use Pyth. Th      Log On


   

Question 276663: Given a square, construct another square whose area will be 5 times the area of the original square. Make a sketch and describe the construction step by step. Hint: Use Pyth. Thrm. to obtain the side of the new square.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If the sides of the 1st square are x, then
A%5B1%5D+=+x%5E2
I want the second square to have 5 times this area, so
A%5B2%5D+=+5A%5B1%5D
A%5B2%5D+=+5x%5E2 or
A%5B2%5D+=+%28sqrt%285%29%2Ax%29%5E2
So, each side of the 2nd square is sqrt%285%29%2Ax
To construct this, you need some way of drawing a line
that has length = sqrt%285%29%2Ax
One way to do it is to draw a line that is the same length
as x. Then draw a line perpendicular to it of length 2x
Then draw the hypotenuse of this right triangle. By pythagorean
theorem, x%5E2+%2B+%282x%29%5E2+=+h%5E2
h%5E2+=+5x%5E2
h+=+sqrt%285%29x
Now construct a square with sides = h