Question

The following sides of triangle upper A upper C upper B are labeled: upper A upper C is 13, and upper B upper C is lower x. Upper A upper D is labeled 5. Right angle symbols are drawn at angle upper B upper A upper C and angle upper A upper D upper C.


Use the steps from the proof of the Pythagorean Theorem to find x.

(1 point)
Responses

x=1698

x equals Start Fraction 169 over 8 End Fraction

x=16912

x equals Start Fraction 169 over 12 End Fraction

x=12

x equals 12

x=169144

x equals Start Fraction 169 over 144 End Fraction
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Answer 1

Let AC = b = 13, BC = c = x, and AD = h = 5 (AD is the altitude to hypotenuse). If p = CD, then b^2 = c p so p = b^2/c = 169/x. Also h^2 = p(c − p). Thus

25 = (169/x)(x − 169/x) = 169(x^2 − 169)/x^2.

So 25x^2 = 169x^2 − 169^2 ⇒ 144x^2 = 169^2 ⇒ x = 169/12.

Answer: x = 169/12.