Answer: The length of AC is approximately 5.196 units.
Explanation:
To find the length of AC, we can use the fact that DE is parallel to AC and AD is parallel to FE, which forms a pair of corresponding angles. Therefore, we can set up a proportion using the fact that corresponding angles are congruent.
DE/AC = AD/FE
We know that DE = 5 and AD = 6, so we can substitute these values into the proportion:
5/AC = 6/FE
We can cross-multiply and solve for AC:
5 * FE = 6 * AC
Next, using the fact that triangle ABC is a triangle, we can use the Pythagorean theorem to find the value of FE.
AB^2 + BC^2 = AC^2
17^2 + BC^2 = (AC)^2
289 + BC^2 = AC^2
Now, substitute the value of FE into the equation we have,
5 * sqrt(AC^2 - 289) = 6 * AC
multiply the both sides of the equation by the reciprocal of 5,
sqrt(AC^2 - 289) = (6/5) * AC
Square both sides of the equation,
AC^2 - 289 = 36/25 * AC^2
subtract the left side from the right side
-289 = -(36/25) * AC^2
divide both sides by -(36/25)
AC = sqrt(289/(1-(36/25)))
AC = sqrt(289/11/25)
AC = sqrt(289/275)
AC = sqrt(289/11)
AC = sqrt(26)
AC = approx 5.196152422706632
Therefore, the length of AC is approximately 5.196 units.