SOLUTION: Find the length of the side of a square whose diagonal is 12 feet longer than The length of a side. Express the answer exactly and to the nearest hundredth

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Question 363811: Find the length of the side of a square whose diagonal is 12 feet longer than
The length of a side. Express the answer exactly and to the nearest hundredth
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi, 

Let x represent the length of each side of the square. (x+12ft) the diagonal.

applying the Pythagorean theorem (with the diagonal being the hypotenuse)

x^2 + x^2 = (x + 12)^2

2x^2 = x^2 + 24x + 144ft^2

x^2 -24x - 144  = 0

using the quadratic equation to solve

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%2824+%2B-+sqrt%28+1152+%29%29%2F%282%29+

x+=+%2824+%2B-+sqrt%28+64%2A18+%29%29%2F%282%29+

x+=+%2824+%2B-+8%2Asqrt%28+18+%29%29%2F%282%29+

x+=+12%2B-+4%2Asqrt%28+18+%29

x+=+12%2B-+16.971

x = 28.971

x = -4.971