Question 205907
Hazel has a screen door whose height is 4 feet more than its width. She wishes to stabilze the door by attaching a steel cable diagonally. If the cable measures sqrt194/2ft, what are the dimensions of the door?
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Let w = width of door
then
w+4 = length of door
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From Pythagorean theorem we know:
{{{ w^2 + (w+4)^2 = (sqrt(194)/2)^2 }}}
{{{ w^2 + (w^2+8w+16) = 194/4 }}}
{{{ 2w^2 + 8w + 16  = 194/4 }}}
{{{ 8w^2 + 16w + 64  = 194 }}}
{{{ 8w^2 + 16w - 130  = 0 }}}
{{{ 4w^2 + 8w - 65 = 0 }}}
Applying the quadratic equation we get:
w = {3.153, -5.153}
Throwing out the negative solution we're left with:
w = 3.153 feet (width)
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Length:
w+4 = 3.153 + 4 = 7.153 feet (length)
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Details of quadratic:
*[invoke quadratic "w", 4, 8, -65 ]