Question 548519
x = height
x+4 = width
20 = hypotenuse
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20^2 = x^2 + (x+4)^2
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400 = x^2 + x^2 + 8x + 16
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0 = 2x^2 +8x - 384
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2x^2 +8x - 384 = 0
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x^2 + 4x -192 = 0
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factor
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(x-12)(x+16) = 0
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zeroes of x = 12 or -16
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{{{ graph(500,500,-20,20,-200,50,x^2+4*x-192) }}}
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x = -16 is not applicable
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x = 12 is the height of the span
x+4 = 16 is the width of the span
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Check using the Pythagorean formula.
12^2 + 16^2 = 144+256 = 400
20^2 = 400
Correct.
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Done.