A right-angled triangle has sided of lengths (x + 5)cm, (x - 3)cm and 9cm. Calculate the value of x. Give your answer to 3 significant figures.
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(x+5)^2 + (x-3)^2 = 9^2
(x^2 + 10x + 25) + (x^2 - 6x + 9) = 81
2x^2 + 4x + 34 = 81
2x^2 + 4x - 47 = 0
Quadratic:
[-4 +/- sqrt(4^2 - 4*2*(-47))]/(2*2)
[-4 +/- sqrt(392)]/4
-1 +/- sqrt(392)/4
x = (3.95 and -5.95)
Validating against
(x - 3) and (x + 5)
(3.95 - 3) = 0.95
(3.95 + 5) = 8.95
(-5.95 - 3) = -8.95 --> cannot have negative length
(-5.95 + 5) = -0.95 --> cannot have negative length
only x = 3.95 is valid
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