"Find the perimeter of the figure, where AC=26, AD=BF, and D is the midpoint of AC. Round your answer to the nearest tenth."
The answer is 128
find the perimeter of the figure where AC=26 AD=BF, and D is the midpoint of AC. round your answer to the nearest tenth.
To find the perimeter of the figure, we need to first determine the lengths of all the sides.
Since D is the midpoint of AC, we can say that AD = CD = 26/2 = 13.
Now let's consider triangle ABD. From the given information, we know that AD = BF, so BF = 13.
The length of side AB can be calculated using the Pythagorean theorem: AB = √(AD^2 + BD^2).
Substituting the values we have: AB = √(13^2 + 13^2) = √(169 + 169) = √(338) ≈ 18.384.
Now we can find the perimeter by adding up all the side lengths: Perimeter = AB + BF + FA + AC.
Since AC = 26 and AD = CD = 13, we know that AC = AD + CD. Therefore, AC = 13 + 13 = 26.
FA is the same length as AC, so FA = 26.
Plugging in the values: Perimeter = 18.384 + 13 + 26 + 26.
Simplifying: Perimeter = 18.384 + 13 + 52 ≈ 83.384.
Rounding to the nearest tenth: Perimeter ≈ 83.4.
Therefore, the perimeter of the figure is approximately 83.4 units.